The vertex coloring of local antimagic total labeling on corona product graphs

• Published in: Journal of physics. Conference series 2021-03, Vol.1836 (1), p.12020
• Main Authors: Agustin, Ika Hesti, Dafik, Nisviasari, Rosanita, Alfarisi, Ridho, Marsidi
• Format: Article
• Language: English
• Subjects: Apexes; Graph coloring; Graph theory; Graphs; Labeling; Physics; Vertex sets
• ISSN: 1742-6588; 1742-6596
• DOI: 10.1088/1742-6596/1836/1/012020

Let G be a graph with the vertex set V(G) and edge set E(G). A function h is a bijective function of domain the union of vertex set and edge set of G and range the natural number {1, 2, 3,… , |V(G)| + |E(G)|. We called the function h as a vertex local antimagic total labeling if for any two adjacent vertices x and x ‘, w(x) = w(x’), where w(x) = ∑ e∈(x) h( e ) + h(x), and E(x) is the set of edges which are incident to x. It is considered to be a proper coloring on vertices of graph G if we assign colour to all vertices with w(x). The minimum number of colors by the vertex local antimagic total labeling of G is called the vertex local antimagic chromatic number, denoted by X la t(G). We study on the vertex local antimagic total labeling of graphs and determined chromatic number on some corona product graphs, namely corona (G © C m ) where G is isomorphis with path, star, broom, cycle, and sunlet graph.