InPrime: Indonesian Journal of Pure and Applied Mathematics
type: channel
description: InPrime: Indonesian Journal of Pure and Applied Mathematics is a peer-reviewed journal published online two times a year in the areas of Pure and Applied Mathematics. The journal stresses mathematics articles devoted to unsolved problems and open questions arising in chemistry, physics, biology, engineering, behavioral science, and all applied sciences. All articles will be reviewed by experts before being accepted for publication. Each author is solely responsible for the content of published articles.
publisher: Department of Mathematics, Faculty of Sciences and Technology, UIN Syarif Hidayatullah
language: en
publication name: InPrime: Indonesian Journal of Pure and Applied Mathematics
issn: 2686-5335
items: Scalability and Cost Efficiency Analysis of Distributed Logistic Regression on Low-Power Clusters Using Apache Spark
items: Fair Secure Roman Dominating Function in Graphs
items: The Influence of the Binary Process Threshold on the BCBimax Algorithm in Finding Optimal BC
items: A Long-Term Dynamics of Chikungunya Transmission with Chronic Infection: Global Stability Analysis of An SICR-SI Model
items: Optimal Control Analysis of a Human-Animal Nipah Virus Transmission Model
items: Multi-Depot Vehicle Routing with Heterogeneous Vehicles using Nearest Neighbor Combined with Simulated Annealing
items: Metric Dimension of Graphs Djembe (Dj_n)
items: Spatial Bayesian Small Area Estimation of Stunting Prevalence at the Subdistrict Level
items: The Locating Chromatic Number of Pentagonal Circular Ladder Graph PCLn
items: Bivariate Binary Logistic Regression Analysis for Modeling Educational Level and Employment Status in Central Java
items: The Locating Chromatic Number of Zigzag Graph Z_n
items: Sombor Index, Randic Index, and Forgotten Index of Fuzzy Coprime Graph on Dihedral Group
items: Survival Analysis of Stroke Incidence in National Health Insurance Participants from 2015–2020
items: The First Zagreb Index and the Narumi-Katayama Index of the Non-Commuting Graph on the Group U_{6n}
items: Error-Resilient Quantum Machine Learning for Real-World Optimization Problems in Finance and Supply Chain Networks
items: Local Metric Dimension of Certain Operation of Generalized Petersen Graph
items: A Multidimensional Approach for Solving Multi-Objective Linear Programming Problems
items: Integrating Spatial Autoregressive Exogenous with Ordinary Kriging for Improved Rainfall Prediction in Java: Enhancing Accuracy with Climate Variables and Spatial Autocorrelation
items: Completely Closed Filter in BN -Algebra
items: Machine Learning for Cybersecurity: Web Attack Detection (Brute Force, XSS, SQL Injection)
items: A Scalable and Privacy-Enhanced Federated Learning Framework with Adaptive Trade-offs Between Communication Efficiency, Privacy Guarantees, and Model Performance in Non-IID Environments
items: Performance Parameters of the FM/FM/1 Queue with a Priori Impatience by the Soft Alpha-Cut Method
items: A Study on Sentiment Analysis of Public Response to The New Fuel Price Policy In 2022: A Support Vector Machine Approach
items: On Codes Over R and its Bounds of Some Kind of Block Repetition Codes in R
items: The Optimal Bonus-Malus System: Case of The Democratic Republic of Congo
items: Fuzzy Unsupervised Artificial Learning Based on Credibilistic Fuzzy C-Means
items: A Comparative Analysis of ARCH/GARCH and Decomposition-ARIMA Models for Gold Price Forecasting in Indonesia
items: A Bibliometric Analysis of Mathematical Problem-Solving: A State of The Art
items: Rainbow Connection Number of Octopus Iteration Graphs
items: The Total Irregularity Strength of a Comb Product of Stars

Scalability and Cost Efficiency Analysis of Distributed Logistic Regression on Low-Power Clusters Using Apache Spark
type: item
description: The limited availability of large-scale computing infrastructure, combined with the high acquisition, operational, and energy costs of conventional GPU-based servers, remains a significant challenge for AI model training and big data learning in resource-constrained educational and research environments. To address this issue, this study proposes and evaluates a horizontally scalable low-power cluster architecture based on Apache Spark for distributed logistic regression training. The novelty of this research lies in the integrated evaluation of scalability performance and computational cost efficiency of Single Board Computer (SBC)-based clusters under varying data complexity scenarios. Experiments were conducted using binary and multiclass datasets by varying the number of observations, feature dimensionality through feature hashing, and the number of classes, with cluster configurations ranging from one to four nodes. Performance was assessed using training time, speedup, parallel efficiency, and electricity cost metrics. Results show that increasing dataset size and feature dimensionality substantially increases computational workload; however, horizontal scaling effectively reduces training time, particularly for high-dimensional and multiclass datasets. The best scalability performance was achieved on the multiclass dataset, where training time decreased by up to 46.98% when scaling from one to four nodes. Although parallel efficiency declined due to communication and synchronization overhead, the system maintained low energy consumption and operational cost. These findings demonstrate that low-power distributed clusters provide a scalable and cost-efficient alternative infrastructure for AI and big data learning in institutions with limited computational resources. Abstrak Keterbatasan ketersediaan infrastruktur komputasi skala besar, yang disertai dengan tingginya biaya pengadaan, operasional, dan konsumsi energi dari server berbasis GPU konvensional, masih …
subject: Articles
  topic: section
subject: Distributed logistic regression
  topic: keywords
subject: Efficiency
  topic: keywords
subject: Horizontal scalability
  topic: keywords
creator: Arjuananta Malik
creator: Taufik Edy Sutanto
creator: Muhaza Liebenlito
creator: Mohamad Irvan Septiar Musti
rights: Copyright (c) 2026 Arjuananta Malik, Taufik Edy Sutanto, Muhaza Liebenlito, Mohamad Irvan Septiar Musti https://creativecommons.org/licenses/by-sa/4.0
date: 2026-05-31
publication date: 2026-05-31
starting page: 85
ending page: 105
doi: 10.15408/inprime.v8i1.50999

Fair Secure Roman Dominating Function in Graphs
type: item
description: Let G=(V(G),E(G)) be a graph and let ϕ:V(G)→{0,1,2} be a function on G. For each i∈{0,1,2}, let V_i={v∈V(G):ϕ(v)=i}. Then ϕ can be represented as ϕ=(V_0,V_1,V_2). A function ϕ is a fair secure Roman dominating function (FScRDF) on G provided that for every v∈V_0, there exists u∈V_2 such that d_G (u,v)=1, ϕ^*=(V_0∖{v}," " V_1∪{v,u}," " V_2∖{u}) is a Roman dominating function (RDF) on G, and for every x,y∈V_0, ∣N_G (x)∩V_2∣=∣N_G (y)∩V_2∣≥1. The weight of FScRDF ϕ on G, denoted by ω_G^FScR (ϕ), is defined as the sum ω_G^FScR (ϕ)=∑_(x∈V(G))▒〖ϕ(x)=∣〗 V_1∣+2∣V_2∣. The fair secure Roman domination number of G is defined as the minimum weight of an FScRDF ϕ on G, and is denoted by γ_FScR (G), that is, γ_FScR (G)=min⁡{ω_G^FScR (ϕ):ϕ" is an FScRDF on " G}. Every FScRDF ϕ on G that satisfies ω_G^FScR (ϕ)=γ_FScR (G) is called a γ_FScR-function on G. In this paper, the authors introduce the idea of fair secure Roman domination in graphs as a new parameter and discuss some important combinatorial results. Abstrak Misalkan G=(V(G),E(G)) adalah graf dan ϕ:V(G)→{0,1,2} adalah fungsi di G. Untuk setiap i∈{0,1,2}, misalkan V_i={v∈V(G):ϕ(v)=i}. Fungsi ϕ dapat disajikan dalam bentuk ϕ=(V_0,V_1,V_2). Fungsi ϕ dikatakan suatu fungsi mendominasi Roman aman cukup (fair secure Roman dominating function; FScRDF) di G apabila untuk setiap v∈V_0, terdapat u∈V_2 sehingga d_G (u,v)=1, ϕ^*=(V_0∖{v}," " V_1∪{v,u}," " V_2∖{u}) adalah suatu fungsi mendominasi Roman (Roman dominating function; RDF) di G, dan untuk setiap x,y∈V_0, ∣N_G (x)∩V_2∣=∣N_G (y)∩V_2∣≥1. Bobot dari FScRDF ϕ di G, dinotasikan dengan ω_G^FScR (ϕ), didefinisikan sebagai jumlah ω_G^FScR (ϕ)=∑_(x∈V(G))▒〖ϕ(x)=∣〗 V_1∣+2∣V_2∣. Bilangan dominasi Roman aman cukup dari G didefinisikan sebagai bobot minimum dari suatu FScRDF ϕ di G, dan dinotasikan dengan γ_FScR (G), yakni, γ_FScR (G)=min⁡{ω_G^FScR (ϕ):ϕ" adalah suatu FScRDF di " G}. Setiap FScRDF ϕ di G yang memenuhi ω_G^FScR (ϕ)=γ_FScR (G) disebut suatu fungsi-γ_FScR di G. Dalam paper ini…
subject: Articles
  topic: section
subject: Fair domination
  topic: keywords
subject: Fair secure Roman dominating function
  topic: keywords
subject: Fair secure Roman domination number
  topic: keywords
subject: Roman dominating function
  topic: keywords
subject: Secure domination
  topic: keywords
creator: Leomarich Casinillo
creator: Emily L. Casinillo
rights: Copyright (c) 2026 Leomarich Casinillo, Emily L. Casinillo https://creativecommons.org/licenses/by-sa/4.0
date: 2026-05-31
publication date: 2026-05-31
starting page: 71
ending page: 84
doi: 10.15408/inprime.v8i1.50904

The Influence of the Binary Process Threshold on the BCBimax Algorithm in Finding Optimal BC
type: item
description: Selecting an appropriate threshold is crucial in the binarization process because it directly affects the quality of biclusters generated by the BCBimax algorithm. However, studies comparing thresholding strategies for optimal bicluster formation are still limited. Therefore, this study proposes an ASR-based evaluation framework to analyze the effect of several thresholding methods on biclustering performance. This study uses 2024 fruit production data from 34 provinces and three special regions in Indonesia, with 25 variables representing fruit commodities. Data preprocessing includes scaling and threshold determination using global and variable-based statistical approaches. The novelty of this research lies in the comparative analysis of threshold selection strategies in BCBimax biclustering using Average Spearman’s Rho (ASR) to evaluate bicluster quality. The results show that the variable-wise median produces patterns similar to the global median, while the variable-wise mean yields the same ASR value as the global mean (0.56909). Although the system-generated threshold yields the smallest ASR (0.09533), it produces only one bicluster. These findings highlight the significant influence of threshold selection on the quality and interpretability of biclustering. Abstrak Pemilihan nilai ambang batas yang tepat sangat penting dalam proses binarisasi karena secara langsung mempengaruhi kualitas bicluster yang dihasilkan oleh algoritma BCBimax. Namun, studi yang membandingkan strategi penentuan ambang batas untuk pembentukan bicluster optimal masih terbatas. Oleh karena itu, penelitian ini mengusulkan kerangka evaluasi berbasis ASR untuk menganalisis pengaruh beberapa metode penentuan ambang batas terhadap kinerja biclustering. Penelitian ini menggunakan data produksi buah tahun 2024 dari 34 provinsi dan tiga daerah khusus di Indonesia, dengan 25 variabel yang mewakili komoditas buah. Praproses data meliputi penskalaan dan penentuan ambang batas menggunakan pendekatan…
subject: Articles
  topic: section
subject: BcBimax algorithm
  topic: keywords
subject: Binarization
  topic: keywords
subject: Threshold
  topic: keywords
creator: Femmy Diwidian
creator: I Made Sumertajaya
creator: Indahwati Indahwati
creator: Hari Wijayanto
creator: Bagus Sartono
rights: Copyright (c) 2026 Femmy Diwidian, I Made Sumertajaya, Indahwati Indahwati, Hari Wijayanto, Bagus Sartono https://creativecommons.org/licenses/by-sa/4.0
date: 2026-05-31
publication date: 2026-05-31
starting page: 56
ending page: 70
doi: 10.15408/inprime.v8i1.50887

A Long-Term Dynamics of Chikungunya Transmission with Chronic Infection: Global Stability Analysis of An SICR-SI Model
type: item
description: Climate change and environmental factors have increased the risk of Chikungunya transmission in tropical regions, highlighting the need for mathematical models that capture its long-term epidemiological dynamics. This study proposes a modified SICR-SI compartmental model incorporating a chronic infection stage, where infected individuals may either recover directly or progress to a non-infectious chronic compartment before recovery. The model extends previous Chikungunya transmission frameworks by repositioning the chronic class before recovery and by establishing a new global stability analysis. Qualitative analysis is performed through positivity and invariant-region investigations, derivation of the basic reproduction number using the Next Generation Matrix approach, local stability analysis via eigenvalue and Routh–Hurwitz criteria, and global stability analysis using a Lyapunov function. The analysis shows that the disease-free equilibrium exists and is locally as well as globally asymptotically stable when the basic reproduction number satisfies R_0 < 1, whereas an endemic equilibrium exists and is locally asymptotically stable when R_0 > 1. Numerical simulations based on Chikungunya data from West Java Province, Indonesia, confirm the theoretical findings and indicate a disease-free scenario with R_0 < 1. Sensitivity exploration further demonstrates that increasing transmission probabilities between humans and mosquitoes significantly elevates R_0, potentially driving the system toward endemic persistence. These results emphasize the importance of reducing vector–host transmission intensity as an effective strategy for controlling Chikungunya outbreaks and provide a theoretical foundation for future epidemiological intervention studies. Abstrak Perubahan iklim dan faktor lingkungan telah meningkatkan risiko penularan Chikungunya di daerah tropis, menyoroti perlunya model matematika yang menangkap dinamika epidemiologi jangka panjangnya. Studi ini mengusulkan …
subject: Articles
  topic: section
subject: Chikungunya
  topic: keywords
subject: SICR-SI model
  topic: keywords
subject: Chronic infection
  topic: keywords
subject: Basic reproduction number
  topic: keywords
subject: Lyapunov function
  topic: keywords
subject: Global stability
  topic: keywords
creator: Ghifa Attaya Ulhaq
creator: Eminugroho Ratna Sari
rights: Copyright (c) 2026 Ghifa Attaya Ulhaq, Eminugroho Ratna Sari https://creativecommons.org/licenses/by-sa/4.0
date: 2026-05-31
publication date: 2026-05-31
starting page: 1
ending page: 16
doi: 10.15408/inprime.v8i1.50544

Optimal Control Analysis of a Human-Animal Nipah Virus Transmission Model
type: item
description: This study proposes a novel multi-host SIRS optimal control model for Nipah virus transmission involving bats, pigs, and humans, extending classical SIR/SEIR frameworks by explicitly incorporating cross-species transmission, reinfection, and heterogeneous contact pathways supported by ecological evidence. Unlike uncontrolled epidemic models, the proposed framework integrates three time-dependent interventions: infected-pig culling, human–animal protective measures, and isolation of infected humans, allowing simultaneous evaluation of epidemiological impact and implementation cost. The existence of an optimal control set is established, and Pontryagin’s Maximum Principle is applied to derive the necessary optimality system. Numerical simulations show that coordinated interventions substantially outperform no-control scenarios. The peak number of infected humans decreases from more than 650,000 to approximately 70,000, while the peak number of infected pigs declines from over 68,000 to about 16,000. Control trajectories indicate that strong early implementation of all measures is the most effective strategy, followed by gradual relaxation as prevalence declines, leading to more efficient resource allocation over time. Compared with classical single-host SIR/SEIR models, the proposed model better captures interspecies spillover dynamics and enables evaluation of integrated response policies that cannot be represented in simpler frameworks. These findings demonstrate the importance of coordinated multi-component strategies for mitigating Nipah outbreaks across interacting host populations. A limitation of this study is the use of assumed parameter values in several transmission processes; future work may incorporate data-driven calibration, stochastic effects, spatial mobility, and uncertainty analysis to improve predictive accuracy. Abstrak Penelitian ini mengusulkan model optimal kontrol SIRS multi-host yang baru untuk penularan virus Nipah yang melibatkan kelelawar, …
subject: Articles
  topic: section
subject: Interspecies transmission
  topic: keywords
subject: Nipah virus
  topic: keywords
subject: Optimal control
  topic: keywords
subject: Population dynamics
  topic: keywords
subject: SIRS model
  topic: keywords
creator: Ratna Widayati
creator: Ramya Rachmawati
creator: Yulian Fauzi
creator: Septri Damayanti
creator: Arlin Marsyanda
rights: Copyright (c) 2026 Ratna Widayati, Ramya Rachmawati, Yulian Fauzi, Septri Damayanti, Arlin Marsyanda https://creativecommons.org/licenses/by-sa/4.0
date: 2026-05-31
publication date: 2026-05-31
starting page: 40
ending page: 55
doi: 10.15408/inprime.v8i1.49631

Multi-Depot Vehicle Routing with Heterogeneous Vehicles using Nearest Neighbor Combined with Simulated Annealing
type: item
description: The Vehicle Routing Problem (VRP) is an essential component of contemporary logistics, which becomes more complex as the Multi-Depot Vehicle Routing Problem (MDVRP) and the Multi-Depot Vehicle Routing Problem with a Heterogeneous Fleet (MDVRPHF). The main objective of MDVRPHF is to meet all customer demands while minimizing total distribution costs by using vehicles with varying capacities. This paper proposes a metaheuristic framework that first uses the Nearest Neighbor (NN) algorithm to build initial routes and then employs the Simulated Annealing (SA) algorithm to optimize the arrangement of goods within each vehicle, ensuring capacity limits are met. Computational experiments using real-world inspired data, representing 20 items distributed from a Bandung depot to multiple customers with three heterogeneous vehicle types, showed that the proposed hybrid NN–SA method achieved an 18.4% reduction in total distribution cost compared to the NN method alone. These results indicate that this integrated approach offers a practical, computationally efficient solution to the complexities of MDVRPHF, establishing it as a useful tool for logistics planning. Keywords: Multi-Depot Vehicle Routing Problem; Heterogeneous Fleet; Nearest Neighbor; Simulated Annealing; Metaheuristics. Abstrak Vehicle Routing Problem (VRP) merupakan bagian penting dari logistik kontemporer, yang kompleksitasnya meningkat menjadi Multi-Depot Vehicle Routing Problem (MDVRP) dan Multi-Depot Vehicle Routing Problem with a Heterogeneous Fleet (MDVRPHF). Untuk MDVRPHF, tujuan utamanya adalah memenuhi seluruh permintaan pelanggan sambil meminimalkan biaya distribusi total dengan memanfaatkan kendaraan berkapasitas berbeda. Makalah ini mengusulkan kerangka kerja metaheuristik yang pertama-tama menggunakan algoritma Nearest Neighbor (NN) untuk membentuk rute awal, kemudian algoritma Simulated Annealing (SA) digunakan untuk mengoptimalkan penataan barang di setiap kendaraan agar batas kapasitas terpenuhi. E…
subject: Articles
  topic: section
subject: Multi-Depot Vehicle Routing Problem
  topic: keywords
subject: Heterogeneous Fleet
  topic: keywords
subject: Nearest Neighbor
  topic: keywords
subject: Simulated Annealing
  topic: keywords
subject: Metaheuristics
  topic: keywords
creator: Debby Agustine
creator: Janson Naiborhu
creator: Ikha Magdalena
rights: Copyright (c) 2025 Debby Agustine, Janson Naiborhu, Ikha Magdalena https://creativecommons.org/licenses/by-sa/4.0
date: 2025-11-28
publication date: 2025-11-28
starting page: 213
ending page: 225
doi: 10.15408/inprime.v7i2.47049

Metric Dimension of Graphs Djembe (Dj_n)
type: item
description: Let G=(V,E) be a connected graph. For an ordered set A⊆V(G), the representation of a vertex with respect to A is defined by its distance vector to the vertices of A. A set A is called a resolving set if every pair of distinct vertices in G has distinct representations with respect to A. The minimum cardinality of a resolving set is called the metric dimension of G. In this paper, we determine the metric dimension of the Djembe graph D_(j_n ) for n≥3. By constructing appropriate resolving sets and proving their minimality, we obtain an exact formula for the metric dimension. The obtained value depends on the congruence class of n modulo 4, with a special case occurring when n=7. These results provide a new contribution to the study of metric dimensions for cycle-based graph families and extend the existing literature on graph resolvability. Abstrak Misalkan G=(V,E) adalah suatu graf terhubung. Untuk suatu himpunan terurut A⊆V(G), representasi sebuah simpul terhadap A didefinisikan sebagai vektor jarak simpul tersebut ke setiap simpul dalam A. Himpunan A disebut himpunan pembeda (resolving set) jika setiap pasangan simpul yang berbeda dalam Gmemiliki representasi yang berbeda terhadap A. Kardinalitas minimum dari himpunan pembeda disebut dimensi metrik (metric dimension) dari graf G. Pada artikel ini ditentukan dimensi metrik dari graf Djembe D_(j_n ) untuk n≥3. Metode yang digunakan adalah konstruksi himpunan pembeda dan pembuktian minimalitasnya untuk memperoleh batas atas dan batas bawah yang berimpit. Hasil penelitian menunjukkan bahwa dimensi metrik graf Djembe dapat dinyatakan secara eksak dalam bentuk formula tertutup yang bergantung pada kelas kongruensi n modulo 4, dengan satu kasus khusus ketika n=7. Hasil ini memberikan kontribusi baru dalam kajian dimensi metrik pada keluarga graf berbasis siklus yang belum pernah diteliti sebelumnya serta memperkaya perkembangan teori resolvabilitas graf. Kata Kunci: Dimensi metrik, Himpunan pembeda, Representasi simpul, …
subject: Articles
  topic: section
subject: Metric dimension
  topic: keywords
subject: Resolving set
  topic: keywords
subject: Distance representation
  topic: keywords
subject: Djembe graph
  topic: keywords
subject: Cycle-Based graph
  topic: keywords
creator: Duratul Hayat
creator: Des Welyyanti
creator: Haripamyu Haripamyu
rights: Copyright (c) 2026 Duratul Hayat, Des Welyyanti, Haripamyu Haripamyu https://creativecommons.org/licenses/by-sa/4.0
date: 2026-05-31
publication date: 2026-05-31
starting page: 30
ending page: 39
doi: 10.15408/inprime.v8i1.46894

Spatial Bayesian Small Area Estimation of Stunting Prevalence at the Subdistrict Level
type: item
description: Achieving Sustainable Development Goal (SDG) 3—ensuring healthy lives and promoting well-being for all—requires reliable health indicators at disaggregated levels. However, conventional large-scale surveys often fail to capture local disparities due to limited sample sizes, leading to unreliable small-area estimates. This study proposes a hierarchical Bayesian Small Area Estimation (HB SAE) framework using a beta distribution and spatial Conditional Autoregressive (CAR) priors to estimate sub-district-level stunting prevalence in Banten Province, Indonesia. The model accounts for both the bound nature of prevalence data and spatial dependence across neighboring areas. Using data from the 2023 Indonesian Health Survey and auxiliary variables from the 2024 Village Potential Data (Podes), the proposed approach demonstrates improved analytical performance. Compared to direct estimation, the HB SAE model reduced the number of sub-districts with Relative Standard Errors (RSE) above 25% from 55 to 44, achieving lower Mean Squared Error (MSE) values and more stable estimates. These results confirm that incorporating spatial effects enhances the precision and reliability of stunting prevalence estimates. The findings provide analytically grounded evidence for localized, data-driven interventions to accelerate efforts to reduce stunting and strengthen policy planning at the sub-district level. Keywords: Bayesian hierarchical model; small area estimation; spatial analysis; stunting prevalence; CAR model. Abstrak Pencapaian Sustainable Development Goal (SDG) 3, yaitu menjamin kehidupan yang sehat dan meningkatkan kesejahteraan bagi semua orang, memerlukan indikator kesehatan yang andal hingga tingkat wilayah kecil. Namun, survei berskala besar sering kali tidak mampu menggambarkan variasi lokal akibat keterbatasan ukuran sampel, sehingga menghasilkan estimasi yang tidak stabil pada wilayah kecil. Penelitian ini mengusulkan kerangka kerja Hierarchical Bayesian Small Area Estimat…
subject: Articles
  topic: section
subject: Bayesian hierarchical model
  topic: keywords
subject: small area estimation
  topic: keywords
subject: spatial analysis
  topic: keywords
subject: stunting prevalence
  topic: keywords
subject: CAR model
  topic: keywords
creator: Ita Wulandari
creator: Ede Surya Darmawan
creator: Sofi Zamzanah
rights: Copyright (c) 2025 Ita Wulandari, Ede Surya Darmawan, Sofi Zamzanah https://creativecommons.org/licenses/by-sa/4.0
date: 2025-10-17
publication date: 2025-10-17
starting page: 128
ending page: 143
doi: 10.15408/inprime.v7i2.46491

The Locating Chromatic Number of Pentagonal Circular Ladder Graph PCLn
type: item
description: Locating coloring is a type of vertex coloring applied to connected graphs, where each vertex is assigned a color such that adjacent vertices receive different colors. In this setting, each color corresponds to a color class, which consists of all vertices assigned that color. A central notion in locating coloring is the color code of a vertex, determined by its distances to each color class. A coloring is classified as a locating coloring when every vertex in the graph has a unique color code. The locating chromatic number of a graph is the minimum number of colors needed to achieve such a coloring. The Pentagonal Circular Ladder graph is a structure formed by combining a circular graph with pentagonal components. This article examines the locating chromatic number of the Pentagonal Circular Ladder graph and provides an analysis of the behavior of locating colorings within this graph family. Keywords: Locating chromatic number; Partition; Locating coloring; Color code; Pentagonal Circular Ladder Graph. Abstrak Pewarnaan lokasi merupakan jenis pewarnaan titik yang diterapkan pada graf terhubung, di mana setiap titik diberi warna sehingga titik-titik yang bertetangga tidak memiliki warna yang sama. Dalam konteks ini, setiap warna membentuk sebuah kelas warna yang terdiri atas seluruh titik yang diberi warna tersebut. Salah satu konsep utama dalam pewarnaan lokasi adalah kode warna suatu titik, yang ditentukan berdasarkan jaraknya terhadap setiap kelas warna. Suatu pewarnaan disebut pewarnaan lokasi apabila setiap titik dalam graf memiliki kode warna yang berbeda. Bilangan kromatik lokasi dari suatu graf didefinisikan sebagai jumlah minimum warna yang diperlukan untuk menghasilkan pewarnaan semacam ini. Graf Pentagonal Circular Ladder merupakan struktur graf yang dibentuk melalui penggabungan graf lingkaran dengan komponen-komponen pentagonal. Artikel ini mengkaji bilangan kromatik lokasi dari graf Pentagonal Circular Ladder serta memberikan analisis mengenai perilaku…
subject: Articles
  topic: section
subject: The Locating Chromatic Number
  topic: keywords
subject: Partition
  topic: keywords
subject: Locating Coloring
  topic: keywords
subject: Color Code
  topic: keywords
subject: Pentagonal Circular Ladder Graph
  topic: keywords
creator: Des Welyyanti
creator: Annisa Wahyuni
creator: Haripamyu
rights: Copyright (c) 2025 Des Welyyanti, Annisa Wahyuni, Haripamyu https://creativecommons.org/licenses/by-sa/4.0
date: 2025-11-28
publication date: 2025-11-28
starting page: 202
ending page: 212
doi: 10.15408/inprime.v7i2.46473

Bivariate Binary Logistic Regression Analysis for Modeling Educational Level and Employment Status in Central Java
type: item
description: Education and employment are two essential components of human development, yet studies that simultaneously examine both outcomes in the context of Central Java remain limited. This research makes a novel contribution by applying bivariate binary logistic regression to jointly model educational attainment and employment status, an approach that has not been previously used for the Central Java population. Using 3,874 observations from the 2024 National Labor Force Survey (Sakernas), the study incorporates two binary response variables and ten predictors to capture the interdependence between education and labor market outcomes. The independence test confirms a significant association between the two responses, supporting the need for a joint modeling framework. Parameter estimation using the Maximum Likelihood method, followed by partial and simultaneous likelihood ratio testing, reveals that marital status and type of institution significantly and simultaneously affect both educational attainment and employment status. The final model achieves classification accuracies of 85.932% and 80.356%, demonstrating strong predictive performance. This study contributes to the literature by presenting an integrated statistical approach that enhances our understanding of how sociodemographic and institutional factors jointly influence human capital and labour participation in Central Java. Keywords: Educational level; Employment status; Bivariate binary logistic regression; Maximum Likelihood method. Abstrak Pendidikan dan pekerjaan adalah dua komponen penting dari pembangunan manusia, namun studi yang secara bersamaan memeriksa kedua hasil dalam konteks Jawa Tengah masih terbatas. Penelitian ini memberikan kontribusi baru dengan menerapkan regresi logistik biner bivariat untuk memodelkan bersama pencapaian pendidikan dan status pekerjaan, suatu pendekatan yang belum pernah digunakan sebelumnya untuk populasi Jawa Tengah. Dengan menggunakan 3.874 observasi dari Survei Angkatan…
subject: Articles
  topic: section
subject: Educational level
  topic: keywords
subject: Employment status
  topic: keywords
subject: Bivariate binary logistic regression
  topic: keywords
subject: Maximum Likelihood method
  topic: keywords
creator: Vera Maya Santi
creator: Farah Fadhilah Ridana
creator: Bagus Sumargo
rights: Copyright (c) 2025 Vera Maya Santi, Farah Fadhilah Ridana, Bagus Sumargo https://creativecommons.org/licenses/by-sa/4.0
date: 2025-11-22
publication date: 2025-11-22
starting page: 181
ending page: 192
doi: 10.15408/inprime.v7i2.46464

The Locating Chromatic Number of Zigzag Graph Z_n
type: item
description: The locating chromatic number is a concept developed from vertex coloring and the partition dimension of a graph, first studied by Chartrand et al. (2002). A connected graph G is said to have a locating coloring when each vertex is assigned a color such that the resulting color code defined by its distances to every color class is unique. The minimum number of colors that satisfies this condition is known as the locating chromatic number, denoted by χ_L (G). This study investigates the value of χ_L for the zigzag graph Z_n with n≥3. Although colorings have been studied for various families of graphs, no explicit characterization of zigzag graphs has been established. Our analysis shows that Z_3 has a locating chromatic number of 3, while for all n≥4, the value increases to 4. These results provide the first complete characterization of locating colorings on zigzag graphs and contribute to the broader study of location-based parameters in graphs with structured topology. Keywords: Locating chromatic number; Zigzag graph; Color code. Abstrak Bilangan kromatik lokasi merupakan konsep pengembangan dari pewarnaan titik dan dimensi partisi suatu graf yang pertama kali dikaji oleh Chartrand dkk (2002). Sebuah graf terhubung Gdikatakan memiliki pewarnaan lokasi apabila setiap titik diberi warna sedemikian rupa sehingga kode warna yang dibentuk berdasarkan jaraknya terhadap setiap kelas warna bersifat unik. Banyaknya warna minimum yang memenuhi kondisi tersebut disebut bilangan kromatik lokasi, dilambangkan dengan χ_L (G). Penelitian ini mengkaji nilai χ_L pada graf zig-zag Z_n untuk n≥3. Walaupun sejumlah keluarga graf telah diteliti sebelumnya dalam konteks pewarnaan lokasi, graf zig-zag belum pernah memperoleh karakterisasi yang jelas. Hasil analisis menunjukkan bahwa Z_3 memiliki bilangan kromatik lokasi adalah 3, sedangkan untuk semua n≥4, nilai tersebut menjadi 4. Temuan ini memberikan karakterisasi lengkap pertama untuk pewarnaan lokasi pada graf zig-zag dan memperkay…
subject: Articles
  topic: section
subject: Locating chromatic number
  topic: keywords
subject: Zigzag graph
  topic: keywords
subject: Color code
  topic: keywords
creator: Vella Sagita Putri
creator: Des Welyyanti
creator: Haripamyu
rights: Copyright (c) 2025 Vella Sagita Putri, Des Welyyanti, Haripamyu https://creativecommons.org/licenses/by-sa/4.0
date: 2025-11-28
publication date: 2025-11-28
starting page: 193
ending page: 201
doi: 10.15408/inprime.v7i2.46443

Sombor Index, Randic Index, and Forgotten Index of Fuzzy Coprime Graph on Dihedral Group
type: item
description: This research investigates the topological indices—Sombor, Randic, and Forgotten—of the fuzzy coprime graph constructed from dihedral groups. These indices, which quantify graph structural properties, have important applications in mathematical chemistry and algebraic graph theory. The study begins by defining fuzzy graphs and coprime graphs, and then introduces the fuzzy coprime graph as a combination of both. Focusing on the dihedral group D_{2n}, with n=p where p is an odd prime, the paper classifies vertices and edges based on their membership values and determines the degree of each vertex. Using these classifications, general formulas for each index are derived. The results show that the fuzzy prime-coprime graph of the dihedral group forms a complete tripartite graph, enabling explicit computation of the Sombor index, Randic index, and Forgotten index. This work extends previous studies by integrating fuzziness into group-based graph representations, offering a new approach to analyzing algebraic structures through topological indices. The findings provide a foundation for future exploration of fuzzy algebraic graphs and their applications in mathematical modeling. Abstrak Penelitian ini menyelidiki indeks topologis—Sombor, Randić, dan Forgotten—pada graf koprima fuzzy yang dibangun dari grup dihedral. Indeks-indeks ini, yang mengukur properti struktural graf, memiliki aplikasi penting dalam kimia matematika dan teori graf aljabar.Studi ini dimulai dengan mendefinisikan graf fuzzy dan graf koprima, kemudian memperkenalkan graf koprima fuzzy sebagai kombinasi keduanya. Dengan fokus pada grup dihedral D_{2n}, dengan n=p dengan p adalah bilangan prima ganjil), penelitian mengklasifikasikan simpul dan sisi berdasarkan nilai keanggotaannya serta menentukan derajat setiap simpul. Berdasarkan klasifikasi ini, rumus umum untuk setiap indeks diturunkan Hasil penelitian menunjukkan bahwa graf koprima fuzzy dari grup dihedral membentuk struktur graf tripartit lengkap, s…
subject: Articles
  topic: section
subject: Fuzzy graph
  topic: keywords
subject: Dihedral group
  topic: keywords
subject: Coprime graph
  topic: keywords
subject: Sombor index
  topic: keywords
subject: Randic index
  topic: keywords
subject: Forgotten index
  topic: keywords
creator: Gusti Yogananda Karang
creator: I Gede Adhitya Wisnu Wardhana
creator: Ni Wayan Switrayni
rights: Copyright (c) 2026 Gusti Yogananda Karang, I Gede Adhitya Wisnu Wardhana, Ni Wayan Switrayni https://creativecommons.org/licenses/by-sa/4.0
date: 2026-05-31
publication date: 2026-05-31
starting page: 17
ending page: 29
doi: 10.15408/inprime.v8i1.46437

Survival Analysis of Stroke Incidence in National Health Insurance Participants from 2015–2020
type: item
description: This study aims to analyze the survival of stroke patients enrolled in the National Health Insurance (Jaminan Kesehatan Nasional, JKN) program and factors affecting it during the 2015–2020 period. Survival analysis was utilized using the Kaplan-Meier estimator and the Cox Proportional Hazards model. The dataset consisted of 12,773 stroke patients sampled from BPJS Kesehatan administrative records. The results indicate that since being registered as BPJS Kesehatan participants or from the baseline year 2015, stroke patients had an average survival time of 2,264 days, with a 95% confidence interval between 2,240 and 2,287 days. The Cox model revealed that patients aged 18–35, 36–50, 51–65, and >65 had Hazard Ratios (HR) of 1.30, 1.69, 2.47, and 3.52, respectively. Female patients exhibited a lower risk of death (HR = 0.81) than males. Employment segment effects were modest, and regional disparities were observed, with the Eastern region showing a higher risk (HR = 1.29). Comorbidities further increased hazards, with hypertension (HR = 1.70) and diabetes (HR = 2.17) significantly raising mortality risk. As one of the first large-scale survival analyses using JKN national data, this study offers novel evidence on key determinants of stroke outcomes in Indonesia. Its findings highlight critical risk factors and support more targeted, data-driven strategies for stroke prevention under universal health coverage. Keywords: Cox Proportional Hazard; Kaplan-Meier; National Health Insurance Agency; Stroke; Survival Analysis. Abstrak Penelitian ini bertujuan untuk menganalisis survival pasien stroke yang terdaftar dalam program Jaminan Kesehatan Nasional (JKN) dan faktor-faktor yang memengaruhinya selama periode 2015–2020. Metode yang digunakan adalah analisis survival dengan pendekatan Kaplan-Meier dan model Cox Proportional Hazards. Data yang dianalisis diambil dari sampel BPJS Kesehatan peserta JKN selama 2015–2020, yang berjumlah 12.773 pasien. Hasil penelitian menunjukkan b…
subject: Articles
  topic: section
subject: Cox Proportional Hazard
  topic: keywords
subject: Kaplan-Meier
  topic: keywords
subject: National Health Insurance Agency
  topic: keywords
subject: Stroke
  topic: keywords
subject: Survival Analysis
  topic: keywords
creator: Irfan Ilmi
creator: Lenny Suardi
rights: Copyright (c) 2025 Lenny Suardi https://creativecommons.org/licenses/by-sa/4.0
date: 2025-07-31
publication date: 2025-07-31
starting page: 101
ending page: 116
doi: 10.15408/inprime.v7i2.49104

The First Zagreb Index and the Narumi-Katayama Index of the Non-Commuting Graph on the Group U_{6n}
type: item
description: This paper introduces a novel approach to computing the First Zagreb and Narumi–Katayama indices for non-commuting graphs associated with specific algebraic groups, specifically focusing on the group U_{6n}. The Narumi–Katayama index, first introduced by Narumi and Katayama in 1984, is a degree-based topological index widely used in the study of various graph properties, including its applications in theoretical chemistry. Non-commuting graphs, where two elements are adjacent if and only if they do not commute, have become an intriguing object of study in recent years. To the best of our knowledge, this is the first study to derive closed-form expressions for the First Zagreb and Narumi–Katayama indices on the non-commuting graph of the group U_{6n}. Building on previous research on the detour index and eccentric connectivity in the graph Γ(U_{6n}), this work makes new contributions by deriving generalized formulas that apply to a broader class of non-commutative groups. Unlike previous studies that focused on commuting or coprime graphs, this research specifically addresses the structure and index computation of non-commuting graphs in a group-theoretic context. The findings offer new theoretical insights into algebraic graph theory by linking degree-based indices with the internal structure of non-abelian groups. These results are expected to expand the understanding of the topological properties of non-commuting graphs and to provide valuable connections to chemical applications. Keywords: Non-commuting graph; First Zagreb Index; Narumi–Katayama Index; graph topology; group structure. Abstrak Artikel ini memperkenalkan pendekatan baru untuk menghitung indeks First Zagreb dan Narumi–Katayama pada graf non-commuting yang terkait dengan grup aljabar tertentu, khususnya berfokus pada grup U_{6n}. Indeks Narumi–Katayama, yang pertama kali diperkenalkan oleh Narumi dan Katayama pada tahun 1984, adalah indeks topologis berbasis derajat yang banyak digunakan dalam studi …
subject: Articles
  topic: section
subject: Non-commuting graph
  topic: keywords
subject: First Zagreb Index
  topic: keywords
subject: Narumi–Katayama Index
  topic: keywords
subject: graph topology
  topic: keywords
subject: group structure.
  topic: keywords
subject: Algebra
  topic: disciplines
creator: Khairatun Hisan
creator: Ibrahim Gambo
creator: I Gede Adhitya Wisnu Wardhana
rights: Copyright (c) 2025 Khairatun Hisan, Ibrahim Gambo, I Gede Adhitya Wisnu Wardhana https://creativecommons.org/licenses/by-sa/4.0
date: 2025-10-05
publication date: 2025-10-05
starting page: 117
ending page: 127
doi: 10.15408/inprime.v7i2.45483

Error-Resilient Quantum Machine Learning for Real-World Optimization Problems in Finance and Supply Chain Networks
type: item
description: The advent of quantum computing has introduced a revolutionary shift in computational paradigms, with the potential to address complex problems beyond the reach of classical systems. However, the practical deployment of quantum solutions is challenged by inherent issues such as noise and decoherence, which hinder their reliability. This study presents a novel error-resilient framework tailored for quantum machine learning (QML) to address optimization problems in finance and supply chain networks. By utilizing hybrid quantum-classical algorithms, the framework mitigates the detrimental effects of quantum noise and enhances computational robustness through advanced techniques like quantum variational circuits. Comprehensive experiments on real-world datasets highlight the framework's ability to outperform conventional methods in solving intricate optimization challenges. The findings demonstrate the transformative potential of quantum-assisted optimization for tackling critical issues in financial modeling and supply chain resilience. In this work, I propose a novel hybrid quantum-classical framework that integrates variational quantum circuits with noise mitigation strategies such as Zero Noise Extrapolation (ZNE), tailored for real-world optimization in finance and supply chain domains. This integrated approach—addressing error resilience and practical scalability together—sets the work apart from existing studies focused solely on theoretical or idealized scenarios. Keywords: Error resilience; Financial modeling; Hybrid algorithms; Optimization challenges; Quantum computing; Quantum machine learning. Abstrak Munculnya komputasi kuantum telah memperkenalkan pergeseran revolusioner dalam paradigma komputasi, dengan potensi untuk mengatasi masalah kompleks di luar jangkauan sistem klasik. Namun, penerapan praktis solusi kuantum ditantang oleh masalah inheren seperti kebisingan dan dekoherensi, yang menghambat keandalannya. Studi ini menyajikan kerangka kerja baru men…
subject: Articles
  topic: section
subject: Error resilience
  topic: keywords
subject: Financial modeling
  topic: keywords
subject: Hybrid algorithms
  topic: keywords
subject: Optimization challenges
  topic: keywords
subject: Quantum computing
  topic: keywords
subject: Quantum machine learning
  topic: keywords
subject:
  topic: disciplines
creator: Milad Rahmati
rights: Copyright (c) 2025 Milad Rahmati https://creativecommons.org/licenses/by-sa/4.0
date: 2025-05-31
publication date: 2025-05-31
starting page: 52
ending page: 65
doi: 10.15408/inprime.v7i1.44960

Local Metric Dimension of Certain Operation of Generalized Petersen Graph
type: item
description: A subset W of V(G) is called a local resolving set of G if r(u│W)≠r(v│W) for every two adjacent vertices u,v∈V(G). The smallest cardinality of all local resolving sets in G is called the local metric dimension of G, denoted by lmd(G). The local resolving set of G with cardinality lmd⁡(G) is called a local basis of G. In this paper, we present a novel study, a topic that has not been extensively explored in previous research, on the local metric dimension of certain operation of generalized Petersen graph sP_(n,1) and determine the lower and upper bounds of "lmd(" sP_(n,m)) with n≥3, s≥1, and 1≤m≤⌊(n-1)/2⌋ . We also show that the lower bound is sharp. Keywords: local resolving set; local metric dimension; generalized Petersen graph. Abstrak Suatu subset W dari V(G) dikatakan himpunan pembeda lokal dari G jika r(u|W) ≠ r(v|W) untuk setiap dua titik bertetangga u,v∈V(G). Kardinalitas terkecil dari semua himpunan pembeda lokal di G disebut dimensi metrik lokal dari G, dinotasikan lmd(G). Himpunan pembeda lokal G dengan kardinalitas lmd(G) disebut basis lokal dari G. Pada artikel ini, disajikan sebuah studi baru, topik yang belum dieskplorasi secara ekstensif dalam penelitian sebelumnya, tentang dimensi metrik lokal dari graf hasil operasi tertentu untuk graf Petersen diperumum sP_(n,1) dan menentukan batas atas dan bawah dari lmd(sP_(n,m)) dengan n≥3, s≥1, dan 1≤m≤⌊(n-1)/2⌋. Kami juga menunjukkan bahwa batas bawah tersebut tajam. Kata Kunci: himpunan pembeda local; dimensi metrik local; graf Petersen diperumum. 2020MSC: 05C12, 05C76
subject: Articles
  topic: section
subject: local resolving set
  topic: keywords
subject: local metric dimension
  topic: keywords
subject: generalized Petersen graph.
  topic: keywords
subject: Graph
  topic: disciplines
creator: Nur Fahri Tadjuddin
creator: Samaneh Nikbakht
rights: Copyright (c) 2025 Nur Fahri Tadjuddin
date: 2025-02-27
publication date: 2025-02-27
starting page: 16
ending page: 24
doi: 10.15408/inprime.v7i1.41320

A Multidimensional Approach for Solving Multi-Objective Linear Programming Problems
type: item
description: Solving multi-objective linear programming problems (MOLPP) is a great challenge because it is essential in many real-life problems, especially manufacturing. Choosing the best solution is the goal of the decision-maker to produce a possibility to improve their ability to decide. Multi-dimensional scaling (MDS) gives this capability to make the right decision. In this study, we develop the MDS method for (MOLPP) in the work of Mrakhan et al. (2020). The method depends on embedding points in R2. Start by building a matrix from a collection of points, and then use clustering to optimize the matrix dimensions and configure the points in R2. The matrix has (k1*2) dimensions, where k1 is the big cluster of the points. Also, a center of points was used to find the scaling points, and then the center of the generated points was used to find a distance from the origin (0,0). Our proposed algorithm offers a structured, efficient compromise solution for MOLPPs, outperforming traditional scalarization-based methods. Keywords: Comprise solution; Multi-dimensional scaling; Multi-objective linear programming; Optimal advanced; Optimal average; Quadratic average. Abstrak Menyelesaikan masalah pemrograman linier multiobjektif (MOLPP) merupakan tantangan besar karena sangat penting dalam banyak masalah kehidupan nyata, terutama manufaktur. Memilih solusi terbaik adalah tujuan pembuat keputusan untuk menciptakan kemungkinan guna meningkatkan kemampuan mereka dalam mengambil keputusan. Penskalaan multidimensi (MDS) memberikan kemampuan ini untuk keputusan yang tepat. Pada studi ini, akan dikembangkan metode MDS untuk (MOLPP) dalam karya Mrakhan et al. (2020). Metode ini bergantung pada penyematan titik-titik di R2: dimulai dengan membangun matriks dari kumpulan titik, lalu gunakan pengelompokan untuk mengoptimalkan dimensi matriks dan mengonfigurasi titik-titik di R2. Matriks memiliki dimensi (k1*2), dimana k1 adalah klaster besar titik-titik. Selain itu, titik pusat digunakan untuk m…
subject: Articles
  topic: section
subject: Comprise solution
  topic: keywords
subject: Multi-dimensional scaling
  topic: keywords
subject: multi-objective linear programming
  topic: keywords
subject: Optimal advanced transformation
  topic: keywords
subject: Optimal average.
  topic: keywords
subject: Quadratic average
  topic: keywords
subject: Professor
  topic: disciplines
creator: Chiya A. Mohammed
creator: Ayad M. Ramadan
rights: Copyright (c) 2025 Ayad M. Ramadan https://creativecommons.org/licenses/by-sa/4.0
date: 2025-05-31
publication date: 2025-05-31
starting page: 66
ending page: 75
doi: 10.15408/inprime.v7i1.45661

Integrating Spatial Autoregressive Exogenous with Ordinary Kriging for Improved Rainfall Prediction in Java: Enhancing Accuracy with Climate Variables and Spatial Autocorrelation
type: item
description: Indonesia is a tropical country with high rainfall influenced by its archipelagic geography and phenomena like El Niño and La Niña. According to the Meteorology, Climatology, and Geophysics Agency (BMKG), La Niña can increase Indonesia's monthly rainfall by 20-40% above normal. Despite numerous existing spatial interpolation methods, there remains a significant research gap in accurately predicting rainfall at unsampled locations, specifically when considering both spatial autocorrelation and multiple climate variables simultaneously. This research proposes Spatial Autoregressive Exogenous Kriging (SAR-X Kriging), a novel hybrid approach that integrates the SAR-X model with Ordinary Kriging to enhance rainfall prediction accuracy. Unlike conventional methods, SAR-X Kriging explicitly captures both spatial dependence and the influence of external climate factors, improving predictive performance. SAR-X Kriging first models spatial dependencies between locations and incorporates exogenous climate variables (surface pressure, air temperature, humidity, wind speed, and solar radiation) to enhance prediction accuracy. It also applies kriging for spatial interpolation. This method was chosen for its robustness in capturing spatial dependence and external influences. The analysis revealed significant spatial dependence across districts/cities in Java Island based on the Moran's Index test. The best SAR-X model, utilizing air temperature and wind speed as exogenous variables, achieved a p-value of 6.0352 × 10-9. Predictions using SAR-X Kriging yielded the lowest Mean Absolute Percentage Error (MAPE) of 3.82%, outperforming the standalone SAR-X method MAPE 4.68% and the Ordinary Kriging method MAPE 3.86%. Practically, these results provide reliable rainfall predictions, enabling better climate-informed decision-making in water resource management, agricultural planning, and flood prevention strategies in Java. Keywords: climate; rainfall; MAPE; SAR-X; SAR-X Kriging. Abstrak …
subject: Articles
  topic: section
subject: climate
  topic: keywords
subject: rainfall
  topic: keywords
subject: MAPE
  topic: keywords
subject: SAR-X
  topic: keywords
subject: SAR-X Kriging
  topic: keywords
subject: Environmental Science
  topic: disciplines
subject: Climatology
  topic: disciplines
subject: Spatial Statistics
  topic: disciplines
subject: Geostatistics
  topic: disciplines
creator: Sandrina Najwa
creator: Dhanti Aurilia Pratiwi
creator: Muhammad Rhafi Ahdian
creator: Ayu Indriani
creator: I Gede Nyoman Mindra
creator: Annisa Nur Falah
creator: Budi Nurani Ruchjana
rights: Copyright (c) 2025 Sandrina Najwa
date: 2025-03-31
publication date: 2025-03-31
starting page: 25
ending page: 43
doi: 10.15408/inprime.v7i1.42070

Completely Closed Filter in BN -Algebra
type: item
description: A BN-algebra (A; *,0) is a non-empty set A equipped with a binary operation * and a constant 0, which satisfies the following axioms: (B1) a*a=0, (B2) a*0=a, and (BN) (a*b)*c=(0*c)*(b*a) for all a,b,c ∈A. A subset I of A is called an ideal in A if it satisfies (i) 0∈I, (ii) if b∈I and a*b∈I imply a∈I, for all a, b ∈ A. This paper presents an original investigation on the completely closed filter in BN-algebra, a topic that has not been extensively explored in previous research. The concepts of filter, closed filter, and completely closed filter in BN-algebra are defined, which can always be associated with the concept of an ideal in BN-algebra. It begins by defining a filter in BN-algebra and then providing additional conditions to make it a closed and completely closed filter. The results show that every filter in BN-algebra has a condition (D), and every non-empty subset of BN1-algebra is a closed filter. Furthermore, every normal ideal in BN-algebra, ideal in Coxeter algebra, and subalgebra in BN1-algebra is a completely closed filter. Keywords: BN-algebra; completely closed filter; filter; ideal. Abstrak BN-Aljabar (A; *,0) adalah himpunan tak kosong A yang dilengkapi dengan operasi biner * dan konstanta 0, yang memenuhi aksioma berikut: (B1) a*a=0,(B2) a*0=a, dan (BN) (a*b)*c=(0*c)*(b*a) untuk setiap a,b,c ∈A. Subhimpunan I dari A disebut ideal di A jika memenuhi: (i) 0∈I, (ii) untuk setiap b∈I dan a*b∈I mengakibatkan a∈I, untuk setiap a,b∈A. Dalam artikel ini, kami menyajikan sebuah studi baru tentang filter tertutup lengkap dalam BN-aljabar, sebuah topik yang belum banyak dieksplorasi dalam penelitian sebelumnya. Konsep filter, filter tertutup, dan filter tertutup lengkap dalam BN-Aljabar didefinisikan, yang mana selalu dapat dikaitkan dengan konsep ideal dalam BN-Aljabar. Dimulai dengan mendefinisikan filter dalam BN-aljabar, kemudian memberikan kondisi tambahan untuk menjadikannya filter tertutup dan filter tertutup lengkap. Hasil yang diperoleh adalah seti…
subject: Articles
  topic: section
subject: BN-algebra
  topic: keywords
subject: completely closed filter
  topic: keywords
subject: filter
  topic: keywords
subject: ideal.
  topic: keywords
subject: Mathematics
  topic: disciplines
subject: Algebra
  topic: disciplines
creator: Andi Rio Ramadhan
creator: Sri Gemawati
creator: Kartini Kartini
rights: Copyright (c) 2025 ANDI RIO RAMADHAN, Sri Gemawati, Kartini Kartini
date: 2025-03-31
publication date: 2025-03-31
starting page: 44
ending page: 51
doi: 10.15408/inprime.v7i1.42170

Machine Learning for Cybersecurity: Web Attack Detection (Brute Force, XSS, SQL Injection)
type: item
description: Security is a top priority in system development, as web portals serve as critical entry points that are frequently targeted by cyber-attacks. Common attack methods include SQL Injection, Cross-Site Scripting (XSS), and Brute Force. The application of machine learning in cybersecurity is growing due to its effectiveness in detecting such threats. This study employs supervised machine learning with six algorithms: K-Nearest Neighbors (KNN), Random Forest, Naïve Bayes, AdaBoost, LightGBM, and XGBoost. The research utilizes the CICIDS2017 and CSE-CICIDS2018 datasets, which contain network traffic data labeled with four categories: Benign, Brute Force, XSS, and SQL Injection. To address the dataset imbalance issue, this study applies Synthetic Minority Oversampling Technique (SMOTE) in conjunction with Principal Component Analysis (PCA) for dimensionality reduction. Performance evaluation is conducted using accuracy, precision, recall, and F1-score metrics, as well as K-Fold Cross Validation, AUC-ROC, and Learning Curve analysis. The results indicate that the Random Forest algorithm achieves the highest classification performance, with an accuracy of 97.77%, precision of 84.07%, recall of 91.96%, and an F1-score of 87.28%. This research contributes by demonstrating the applicability of machine learning in real-time web attack detection, highlighting the advantages of ensemble-based models in handling cybersecurity threats. Additionally, it underscores the importance of dataset preprocessing techniques in enhancing classification performance. Future improvements should focus on optimizing hyperparameters, integrating real-time network traffic analysis, and exploring hybrid models that combine traditional machine learning with deep learning approaches to further enhance detection capabilities. Keywords: machine learning; cybersecurity; web attack detection; random forest; SMOTE; PCA. Abstrak Keamanan merupakan prioritas utama dalam pengembangan sistem, karena portal web b…
subject: Articles
  topic: section
subject: machine learning
  topic: keywords
subject: cybersecurity
  topic: keywords
subject: web attack detection
  topic: keywords
subject: random forest
  topic: keywords
subject: SMOTE
  topic: keywords
subject: PCA.
  topic: keywords
subject: applied mathematics
  topic: disciplines
subject: machine learning
  topic: disciplines
creator: Muhammad Irfa’issurur
creator: Bony Parulian Josaphat
rights: Copyright (c) 2025 Muhammad Irfa’issurur, Muhammad Irfa’issurur, Bony Parulian Josaphat
date: 2025-02-26
publication date: 2025-02-26
starting page: 1
ending page: 15
doi: 10.15408/inprime.v7i1.41025

A Scalable and Privacy-Enhanced Federated Learning Framework with Adaptive Trade-offs Between Communication Efficiency, Privacy Guarantees, and Model Performance in Non-IID Environments
type: item
description: Federated learning (FL) has become a promising paradigm for collaborative machine learning that preserves the privacy of distributed data sources. However, implementing privacy-preserving federated learning (PPFL) in real-world settings poses several critical challenges, particularly in balancing communication efficiency, strong privacy guarantees, and reliable model performance. These issues are further exacerbated in non-IID (non-independent and identically distributed) environments, which are common in decentralized data scenarios. This study introduces a scalable framework for PPFL that incorporates an adaptive mechanism to optimize trade-offs among communication, privacy, and performance, tailored to dynamic, resource-constrained settings. The proposed framework integrates advanced differential privacy techniques with efficient communication strategies and employs robust aggregation algorithms to address data heterogeneity. Analytical evaluations highlight the scalability and effectiveness of the approach, while experimental validations demonstrate its advantages in terms of privacy-accuracy trade-offs across diverse datasets, including applications in healthcare and IoT. This work contributes to enhancing the practicality of FL systems by demonstrating a 6.5% accuracy improvement on CIFAR-10 in non-IID settings, maintaining 87.2% accuracy at a strict privacy budget of ε=1.0, and reducing communication overhead by 40% compared to baselines, addressing key barriers to deployment and setting a foundation for future research in dynamic, privacy-preserving machine learning systems. Keywords: Adaptive algorithms; Data heterogeneity; Differential privacy; Distributed systems; Scalability. Abstrak Pembelajaran terfederasi (Federated learning) telah menjadi paradigma yang menjanjikan untuk pembelajaran mesin kolaboratif yang menjaga privasi sumber data terdistribusi. Namun, penerapan pembelajaran terfederasi yang menjaga privasi (PPFL) dalam dunia nyata menghadapi bebe…
subject: Articles
  topic: section
subject: adaptive algorithms
  topic: keywords
subject: data heterogeneity
  topic: keywords
subject: differential privacy
  topic: keywords
subject: distributed systems
  topic: keywords
subject: scalability
  topic: keywords
subject:
  topic: disciplines
creator: Milad Rahmati
creator: Nima Rahmati
rights: Copyright (c) 2025 Milad Rahmati https://creativecommons.org/licenses/by-sa/4.0
date: 2025-11-15
publication date: 2025-11-15
starting page: 144
ending page: 158
doi: 10.15408/inprime.v7i2.45035

Performance Parameters of the FM/FM/1 Queue with a Priori Impatience by the Soft Alpha-Cut Method
type: item
description: This study investigates the performance parameters of the fuzzy Markovian queueing system FM/FM/1 with a priori impatience using the soft alpha-cut method. The model incorporates the hesitation behavior of customers who decide whether to join a queue based on the expected waiting time. Unlike traditional parametric nonlinear programming approaches that combine multiple fuzzy arithmetics, the proposed method employs a single arithmetic framework based solely on alpha-cuts and interval operations, thereby simplifying and enhancing the computational efficiency. The study develops fuzzy formulations for key performance indicators, including server utilization rate, system throughput, average number of customers in the system and queue, and average waiting and residence times. A numerical application in a banking service context demonstrates the validity and practicality of the approach. The results show that each performance indicator is represented as a fuzzy number characterized by its support, mode, and membership function, allowing greater flexibility in managerial decision-making compared to the classical M/M/1 queueing system. Furthermore, the modal values of the fuzzy indicators coincide with the average values of their classical counterparts, confirming that the classical models are exceptional cases of the fuzzy ones. Keywords: Fuzzy Markovian queue; A priori impatience, Soft alpha-cut method, Performance indicators, Queueing theory. Abstrak Penelitian ini menyelidiki parameter kinerja sistem antrean Markovian fuzzy FM/FM/1 dengan ketidaksabaran apriori menggunakan metode alpha-cut lunak. Model ini menggabungkan perilaku ragu-ragu pelanggan yang memutuskan untuk bergabung dalam antrean berdasarkan perkiraan waktu tunggu. Tidak seperti pendekatan pemrograman nonlinier parametrik tradisional yang menggabungkan beberapa aritmatika fuzzy, metode yang diusulkan menggunakan kerangka kerja aritmatika tunggal yang semata-mata didasarkan pada alpha-cut dan operasi inter…
subject: Articles
  topic: section
subject: Fuzzy Markovian queue
  topic: keywords
subject: A priori impatience
  topic: keywords
subject: Soft alpha-cut method
  topic: keywords
subject: Performance indicators
  topic: keywords
subject: Queueing theory
  topic: keywords
subject: Applied Mathematics
  topic: disciplines
creator: Mudimbiyi Ebondo Mbavu Durac
creator: Mabela Makengo Matendo Rostin
creator: Tawaba Musian Ta – yen Gérard
rights: Copyright (c) 2025 Durac Mudimbiyi Ebondo, Rostin MABELA MAKENGO MATENDO, Gérard Tawaba Musian Tayen https://creativecommons.org/licenses/by-sa/4.0
date: 2025-11-19
publication date: 2025-11-19
starting page: 159
ending page: 180
doi: 10.15408/inprime.v7i2.45346

A Study on Sentiment Analysis of Public Response to The New Fuel Price Policy In 2022: A Support Vector Machine Approach
type: item
description: The Indonesian government's decision to raise fuel prices in 2022, following a global surge in crude oil prices, triggered widespread public debate. Understanding public sentiment toward such policy decisions is essential for determining the appropriate timing of implementation while minimizing negative reactions. This study aims to classify public sentiment regarding the fuel price hike using the Support Vector Machine (SVM) algorithm. Data were collected from Twitter through web scraping using the SNScrape library in Python. A total of 3,000 tweets were gathered and underwent preprocessing steps such as case folding, tokenization, stopword removal, and stemming. The classification model was built in Google Colab using the SVM algorithm to categorize tweets as positive (+) or negative (–). Model performance was evaluated using a confusion matrix, achieving an accuracy of 81.0%. The results showed that 63.6% of public responses were negative, while 36.4% were positive. Additionally, it was observed that the accuracy converged to 81.1% as the number of training iterations increased. The findings were presented through word clouds and pie charts to enhance interpretability, and a simple graphical user interface (GUI) was developed for user interaction. The study indicates that the government’s repeated delays in implementing the price adjustment may have reflected sensitivity to public sentiment. This research demonstrates the potential of sentiment classification as a tool for evidence-based policymaking, offering insights into the social dynamics surrounding policy changes. Future research could expand by incorporating multi-class sentiment categories or real-time data for dynamic policy evaluation. Keywords: Fuel price; Public opinion; Sentiment analysis; Social media; SVM. Abstrak Keputusan pemerintah Indonesia untuk menaikkan harga bahan bakar minyak pada tahun 2022 dan disusul oleh lonjakan harga minyak mentah global, memicu perdebatan publik yang meluas. Memaha…
subject: Articles
  topic: section
subject: Fuel price
  topic: keywords
subject: Public opinion
  topic: keywords
subject: Sentiment analysis
  topic: keywords
subject: Social media
  topic: keywords
subject: SVM
  topic: keywords
subject: Mathematics
  topic: disciplines
subject: Informatics
  topic: disciplines
creator: Niluh Putu Aprillia Puspitadewi Sudarsana Putri
creator: Dwi Shinta Angreni
creator: I Wayan Sudarsana
rights: Copyright (c) 2025 I Wayan Sudarsana, Niluh Putu Aprillia Puspitadewi Sudarsana Putri, Dwi Shinta Angreni https://creativecommons.org/licenses/by-sa/4.0
date: 2025-05-31
publication date: 2025-05-31
starting page: 88
ending page: 100
doi: 10.15408/inprime.v7i1.42717

On Codes Over R and its Bounds of Some Kind of Block Repetition Codes in R
type: item
description: This correspondence determines the lower and upper bounds of the covering radius in some kind of block repetition codes over the ﬁnite ring R=Z_2 Z_*, where Z_*=Z_2+vZ_2+v^2 Z_2, v^3=v. For covering radii of binary and octonary block repetition code over is also discussed. This leads to the convenient formulation of code and arrives at the bounds. Keywords: block repetition codes; covering radius; different weight; finite ring. Abstrak Korespondensi ini menentukan batas bawah dan batas atas dari jari-jari penutup suatu kode blok perulangan pada gelanggang hingga R=Z_2 Z_*, dengan Z_*=Z_2+vZ_2+v^2 Z_2, v^3=v. Dibahas juga jari-jari kode blok perulangan biner dan oktonari atas . Diperoleh rumus untuk kode dan batasnya. Kata Kunci: kode blok perulangan; penutup jari-jari; berat yang berbeda; gelanggang hingga. 2020MSC: 11T71, 94B05, 11H71.
subject: Articles
  topic: section
subject: block repetition codes
  topic: keywords
subject: covering radius
  topic: keywords
subject: different weight
  topic: keywords
subject: finite ring.
  topic: keywords
subject: Mathematics
  topic: disciplines
creator: P Chella Pandian
rights: Copyright (c) 2022 P Chella Pandian
date: 2022-11-04
publication date: 2022-11-04
starting page: 151
ending page: 159
doi: 10.15408/inprime.v4i2.27239

The Optimal Bonus-Malus System: Case of The Democratic Republic of Congo
type: item
description: Abstract Automobile insurance is required in most African nations, and it is the most significant branch in the Democratic Republic of the Congo (DRC); if the automobile branches are poorly managed, this could even result in the insurance company's insolvency. A priori pricing does not improve the danger parameter (the variance), which measures the difference between the estimated model and the observed reality; since the pricing characteristics do not take into account the driver's experience, the portfolio remains heterogeneous. To ensure the insurer's solvency, a more refined post-season pricing model is necessary, one that accounts for driver behavior. Our research introduces an innovative approach to a posteriori pricing in the DRC, using the Bonus-Malus System. In this model, policyholders are divided into classes based on the frequency of claims to preserve the insurer's solvency. The Bonus-Malus System will serve as the basis for the automobile portfolio's a posteriori pricing: the driver who has not declared a claim receives a reduction in his premium in the year tn+1 (Bonus), and the wrong driver who has declared more than one claim will see his premium increased to the year tn+1 (Malus). Inspired by models from Belgium (the class model) and France (the multiplicative model), we develop a Bonus-Malus model applicable to the DRC. The results found that the class system outperforms the other model for the DRC due to its clarity and fairness. We also emphasize the need for SONAS to centralize data to effectively implement this system and optimize motor vehicle claim management. Keywords: bonus-malus; insurance policy; risk; frequency of claims; prior pricing; ex post facto pricing. Abstrak Asuransi mobil diwajibkan di sebagian besar negara Afrika, dan merupakan cabang yang paling signifikan; di Republik Demokratik Kongo (DRC),. Jika cabang mobil dikelola dengan buruk, hal ini bahkan dapat mengakibatkan kebangkrutan perusahaan asuransi. Penetapan harga secara …
subject: Articles
  topic: section
subject: bonus-malus
  topic: keywords
subject: insurance policy
  topic: keywords
subject: risk
  topic: keywords
subject: frequency of claims
  topic: keywords
subject: prior pricing
  topic: keywords
subject: ex post facto pricing.
  topic: keywords
subject: applied mathematics
  topic: disciplines
subject: actuary
  topic: disciplines
creator: Crispin Bukanga Maheshe
creator: Mabela Makengo Matendo Rostin
rights: Copyright (c) 2024 Crispin Bukanga Maheshe, Rostin Mabela Makengo Matendo Rostin
date: 2024-05-31
publication date: 2024-05-31
starting page: 27
ending page: 37
doi: 10.15408/inprime.v6i1.38074

Fuzzy Unsupervised Artificial Learning Based on Credibilistic Fuzzy C-Means
type: item
description: This study proposes an unsupervised artificial learning approach based on the Credibilistic Fuzzy C-Means (CFCM) algorithm to enhance the governance and analysis of oil production data. The research focuses on supporting decision-making in managing oil output from the MOTOBA oil field, operated by PERENCO in Moanda, Democratic Republic of Congo, covering the period from 2018 to 2021. The methodology involves structuring and segmenting production data using the CFCM algorithm, which enables the identification of meaningful production patterns despite the presence of uncertainty and imprecision in the data. The analysis identified three distinct clusters: wells with low production, wells with moderate production, and wells with high production. These clusters offer valuable insights into the variability of well performance and provide a basis for optimizing operational strategies. The credibilistic enhancement of traditional fuzzy clustering allows for more effective handling of data uncertainty, resulting in a robust and interpretable model—particularly beneficial in complex and data-limited environments. This clustering framework supports more refined monitoring, resource allocation, and operational planning, making it well-suited for the dynamic nature of oil field management. Furthermore, the methodology demonstrates potential scalability and applicability to other industrial domains facing similar challenges in data quality and decision-making under uncertainty. Ultimately, this work contributes to the advancement of data-driven governance in natural resource management through a rigorous and adaptable analytical approach. Keywords: Artificial learning; Clustering; Credibilist; Fuzzy C-means; Fuzzy logic. Abstrak Studi ini mengusulkan pendekatan pembelajaran buatan tanpa pengawasan berdasarkan algoritma Credibilistic Fuzzy C-Means (CFCM) untuk meningkatkan tata kelola dan analisis data produksi minyak. Penelitian ini berfokus pada dukungan pengambilan keputusan d…
subject: Articles
  topic: section
subject: Artificial learning
  topic: keywords
subject: Clustering
  topic: keywords
subject: Credibilist
  topic: keywords
subject: Fuzzy C-means
  topic: keywords
subject: Fuzzy logic
  topic: keywords
subject: Applied Mathematics
  topic: disciplines
creator: Kangiama Lwangi Richard
creator: Kafunda Katalayi Pierre
creator: Kabamba Baludikay Blaise
creator: Mabela Makengo Matendo Rostin
creator: Munene Asidi Djonive
rights: Copyright (c) 2025 Richard Albert KANGIAMA https://creativecommons.org/licenses/by-sa/4.0
date: 2025-05-31
publication date: 2025-05-31
starting page: 76
ending page: 87
doi: 10.15408/inprime.v7i1.44234

A Comparative Analysis of ARCH/GARCH and Decomposition-ARIMA Models for Gold Price Forecasting in Indonesia
type: item
description: Gold is considered a low-risk investment, serving as a hedge asset and haven against inflation and economic shocks. While gold prices exhibit an increasing trend in the long term, they are subject to short-term fluctuations. Accurate gold price prediction is crucial for investors to maximize returns. This research aims to identify the most suitable method for forecasting gold prices in Indonesia, comparing the decomposition-ARIMA and ARCH-GARCH models. The findings reveal that the decomposition-ARIMA(2,1,2) method surpasses the GARCH(1,0) model in accuracy. The forecasting results indicate an upward trend in gold prices, with an average IDR of 1,209,214.11. This study demonstrates the superior accuracy of the decomposition-ARIMA method for gold price forecasting in Indonesia, offering valuable insights for investors seeking to optimize their investment strategies. Keywords: ARCH-GARCH model; forecasting; gold; volatility. Abstrak Emas dianggap sebagai investasi berisiko rendah, berfungsi sebagai aset hedge dan safe haven yang aman terhadap inflasi dan guncangan ekonomi. Meskipun harga emas menunjukkan tren peningkatan dalam jangka panjang, harga emas juga dapat mengalami fluktuasi dalam jangka pendek. Prediksi harga emas yang akurat sangat penting bagi investor untuk memaksimalkan keuntungan. Penelitian ini bertujuan untuk mengidentifikasi metode yang paling sesuai untuk meramalkan harga emas di Indonesia, dengan membandingkan model dekomposisi-ARIMA dan model ARCH-GARCH. Temuan menunjukkan bahwa metode dekomposisi-ARIMA(2,1,2) melampaui akurasi model GARCH(1,0). Hasil peramalan menunjukkan adanya tren kenaikan harga emas dengan harga rata-rata Rp 1.209.214,11. Kontribusi studi ini terletak pada demonstrasi akurasi metode dekomposisi-ARIMA yang unggul dalam peramalan harga emas di Indonesia, sehingga menawarkan wawasan berharga bagi investor yang ingin mengoptimalkan strategi investasinya. Kata Kunci: model ARCH-GARCH; prediksi; emas; volatilitas. 2020MSC: 62M10.
subject: Articles
  topic: section
subject: ARCH-GARCH model
  topic: keywords
subject: forecasting
  topic: keywords
subject: gold
  topic: keywords
subject: volatility.
  topic: keywords
subject: Statistics
  topic: disciplines
creator: Ronald Hutajulu
creator: Neli Agustina
rights: Copyright (c) 2024 Neli Agustina, Ronald Hutajulu
date: 2024-11-15
publication date: 2024-11-15
starting page: 158
ending page: 171
doi: 10.15408/inprime.v6i2.40249

A Bibliometric Analysis of Mathematical Problem-Solving: A State of The Art
type: item
description: This study aims to explore research on problem-solving in various countries using complete and systematic bibliometrics, mainly Publish or Perish (PoP) and Vos viewer, to analyze data systematically. This analysis reveals the development of research related to problem-solving to provide new ideas and raise research gaps related to this topic. The data used in 2016-2022 is 2959 articles using keywords, namely problem solving and mathematics. The method used in this study used bibliometric analysis with interconnected keyword maps. Through this bibliometric, researchers can find research trends by the chosen topic, explain the updates that can be presented, and determine research gaps. So, this research is the first step to making it easier for researchers to report the results of previous studies and offer further research. Keywords: bibliometric; mathematics; problem-solving; vos viewer. Abstrak Tujuan penelitian ini untuk mengeksplorasi penelitian tentang pemecahan masalah diberbagai negara dengan menggunakan analisis data bibliometric vos viewer dan publish or perish secara lengkap dan sistematis. Analisis ini mengungkapkan perkembangan penelitian terkait pemecahan masalah untuk memberika ide baru serta memunculkan kesenjangan penelitian terkait topik ini. data yang digunakan pada tahun 2016-2022 sebanyak 2959 artikel. Metode yang digunakan dalam penelitian ini menggunakan analisis bibliometric dengan peta kata kunci yang saling berhubungan. Melalui bibliometric ini peneliti dapat menemukan trend penelitian yang sesuai dengan topik yang dipilih, menjelaskan kebeharuan yang dapat disajikan serta menentukan gap penelitian. Sehingga penelitian ini sebagai langkah awal untuk memudahkan peneliti melaporkan hasil penelitian terdahulu untuk dapat menawarkan penelitian yang berbeda dari penelitian yang sudah ada. Kata Kunci: bibliometrik; matematika; penyelesaian masalah; vos viewer. 2020MSC: 97D50, 97U60.
subject: Articles
  topic: section
subject: bibliometric
  topic: keywords
subject: mathematics
  topic: keywords
subject: problem solving
  topic: keywords
subject: Vos viewer.
  topic: keywords
subject: mathematics
  topic: disciplines
subject:
  topic: disciplines
creator: Shelly Morin
rights: Copyright (c) 2024 Shelly Morin
date: 2024-11-20
publication date: 2024-11-20
starting page: 172
ending page: 193
doi: 10.15408/inprime.v6i2.41418

Rainbow Connection Number of Octopus Iteration Graphs
type: item
description: The rainbow connection number of a graph G denoted by rc(G) is the minimum number of colors used to color the edges in G, such that every pair of vertices is connected by a path with all different colors. In 2008, Chartrand et al. first introduced the concept of rainbow connection numbers. They introduced it as an edge coloring on a graph that refers to the path of each pair of vertices. An octopus graph, with m legs denoted by Om, is a graph constructed from a fan graph Fm and a star graph Sm. The graphs studied in this article are two classes of octopus iteration graphs, namely the octopus chain graph and the octopus ladder graph. The octopus chain graph, denoted by O2(n) is a graph constructed from n copies of O2 and connecting one leg of the i-th copy to the (i+1)-th copy, for every I = 1,2,..., n-1. The octopus ladder graph, denoted by O2'(n) is a graph constructed from graph O2(n) by connecting one of vertex of degree two of the i-th copy to the (i+1)-th copy. In this research, we determine the rainbow connection number of the octopus chain graphs O2(n) and the octopus ladder graphs O2'(n). We obtain that rc(O2(n))=3n, for n >= 1 and rc(O2'(n))=3n-1, for n >= 2. Keywords: classes of octopus iteration graphs; octopus chain graph; octopus ladder graph; rainbow connection number. Abstrak Bilangan terhubung pelangi pada graf G dinotasikan dengan rc(G) merupakan jumlah warna minimum yang digunakan untuk mewarnai sisi pada G, sehingga setiap pasang titik dihubungkan oleh suatu lintasan dengan warna yang berbeda semua. Pada tahun 2008, Chartrand dkk. pertama kali memperkenalkan konsep bilangan terhubung pelangi. Chartrand dkk. memperkenalkannya sebagai pewarnaan sisi pada graf yang mengacu pada lintasan setiap pasang titiknya. Graf gurita dengan m kaki dinotasikan denganOm adalah graf yang dikonstruksi dari graf kipas Fm dan graf bintang Sm. Graf yang dikaji dalam artikel ini merupakan dua kelas graf iterasi gurita, yaitu graf rantai gurita dan graf tangga gurita. Gr…
subject: Articles
  topic: section
subject: classes of octopus iteration graphs
  topic: keywords
subject: octopus chain graph
  topic: keywords
subject: octopus ladder graph
  topic: keywords
subject: rainbow connection number.
  topic: keywords
subject: Mathematic
  topic: disciplines
subject: combinatoric
  topic: disciplines
creator: Desi Rahmadani
creator: Adinda Evelyn Giyanatta
creator: Dina Pratiwi
creator: Mahmuddin Yunus
creator: Vita Kusumasari
rights: Copyright (c) 2024 Adinda Evelyn Giyanatta
date: 2024-11-30
publication date: 2024-11-30
starting page: 205
ending page: 216
doi: 10.15408/inprime.v6i2.41414

The Total Irregularity Strength of a Comb Product of Stars
type: item
description: A totally irregular total k-labeling λ: V U E → {1, 2, ⋯ , k} of a graph G is a labeling where the weights of all distinct vertices and edges are unique. The weight w(x) of a vertex x is defined as the sum of its label and the labels of all edges incident to it, while the weight w(e) of an edge e is the sum of its label and the labels of its two endpoints. The minimum k for which G admits such a labeling is known as the total irregularity strength of G, denoted ts(G). This study focuses on determining ts(G) for specific classes of trees, including the comb product of stars, where the contact vertex is the central vertex of one star, and the triple star graph. Keywords: comb product; star; total irregularity strength; totally irregular total labeling graph. Abstrak Pelabelan k-total tak teratur total λ: V U E → {1, 2, ⋯ , k} dari suatu graf G adalah suatu pelabelan sedemikian sehingga bobot setiap titik dan sisi masing-masing berbeda. Bobot suatu titik w(x) adalah jumlah label titik x dan label setiap sisi yang terkait ke x, dan bobot suatu sisi w(e) adalah jumlah label sisi e dan kedua titik yang terkait ke e. Nilai minimum k sehingga suatu graf G memiliki pelabelan tersesebut dikenal sebagai nilai ketakteraturan total dari G, dinotasikan dengan ts(G). Pada artikel ini, ditentukan nilai ketakteraturan total dari suatu kelas graf pohon, yaitu hasil operasi comb dari graf bintang, dimana titik tetapnya adalah titik pusat graf bintang, dan graf bintang tripel. Kata Kunci: hasil operasi comb; graf bintang, nilai ketakteraturan total; pelabelan total tak teratur total. 2020MSC: 05C78
subject: Articles
  topic: section
subject: comb product
  topic: keywords
subject: star
  topic: keywords
subject: total irregularity strength
  topic: keywords
subject: totally irregular total labeling graph
  topic: keywords
subject: Graph Theory
  topic: disciplines
subject: Graph Labeling
  topic: disciplines
creator: Meilin Imelda Tilukay
creator: Harmanus Batkunde
rights: Copyright (c) 2024 Meilin Imelda Tilukay, Harmanus Batkunde
date: 2024-11-30
publication date: 2024-11-30
starting page: 217
ending page: 224
doi: 10.15408/inprime.v6i2.42188