The Modular Irregularity Strength of C_n⊙mK_1
Abstract
Let G(V, E) be a graph with order n with no component of order 2. An edge k-labeling α: E(G) →{1,2,…,k} is called a modular irregular k-labeling of graph G if the corresponding modular weight function wt_ α:V(G) → Z_n defined by wt_ α(x) =Ʃ_(xyϵE(G)) α(xy) is bijective. The value wt_α(x) is called the modular weight of vertex x. Minimum k such that G has a modular irregular k-labeling is called the modular irregularity strength of graph G. In this paper, we define a modular irregular labeling on C_n⊙mK_1. Furthermore, we determine the modular irregularity strength of C_n⊙mK_1.
Keywords: corona product; cycle; empty graph; modular irregular labeling; modular irregularity strength.
Abstrak
Diberikan graf G(V, E) dengan orde n dengan tidak ada komponen yang berorde 2. Sebuah pelabelan-k sisi α: E(G) →{1,2,…,k} disebut pelabelan-k tak teratur modular pada graf G jika fungsi bobot modularnya wt_ α:V(G) → Z_n dengan wt_ α(x) =Ʃ_(xyϵE(G)) α(xy) merupakan fungsi bijektif. Nilai wt_α(x) disebut bobot modular dari simpul x. Minimum dari k sehingga G mempunyai pelabelan-k tak teratur modular disebut dengan kekuatan ketakteraturan modular dari graf G. Pada tulisan ini, didefinisikan pelabelan tak teratur modular pada C_n⊙mK_1. Lebih lanjut, ditentukan kekuatan ketakteraturan modular dari C_n⊙mK_1.
Kata Kunci: hasil kali korona; lingkaran, graf kosong; pelabelan tak teratur modular; kekuatan ketakteraturan modular.
Keywords
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DOI: 10.15408/inprime.v4i2.26935
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