The Locating Chromatic Number for Amalgamation of Some Complete Graphs
Abstract
The locating chromatic number of a graph is a combination of partition dimension and vertex coloring, where every two adjacent vertices are in different color classes, and all vertices have a unique color code. The amalgamation of a ≥ 2 complete graphs (K_n, n≥ 3) denoted by aK_n is obtained by identifying one vertex from each complete graph. In this paper, we present a novel study, a topic that has not been extensively explored in previous research, on locating chromatic numbers for the amalgamation of complete graphs aK_n for 2 ≤ a ≤ 6 and n≥ 3.
Keywords: locating chromatic number, partition dimension, vertex coloring, color code, amalgamation of complete graph.
Abstrak
Bilangan kromatik lokasi graf merupakan penggabungan dari dimensi partisi dan pewarnaan titik, yang mana setiap dua titik bertetangga berada dalam kelas warna yang berbeda dan semua titik mempunyai kode warna yang unik. Amalgamasi dari a ≥ 2 buah graf lengkap (K_n, n≥ 3) dinotasikan dengan aK_n diperoleh dengan cara menyatukan satu titik dari setiap graf lengkap . Pada paper ini didiskusikan hasil yang belum ada sebelumnya, yaitu bilangan kromatik lokasi amalgamasi graf lengkap aK_n untuk 2 ≤ a ≤ 6 dan n≥ 3 .
Kata Kunci: bilangan kromatik lokasi, dimensi partisi, pewarnaan titik, kode warna, amalgamasi graf lengkap.
2020MSC: 05C12, 05C15
Keywords
References
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DOI: 10.15408/inprime.v6i1.38711
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