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

Abstract

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 Xlat(G). We study on the vertex local antimagic total labeling of graphs and determined chromatic number on some corona product graphs, namely corona (G © Cm) where G is isomorphis with path, star, broom, cycle, and sunlet graph.