Local super antimagic total vertex coloring of some wheel related graphs

Abstract

Let G be a simple and finite graph with vertex set V and edge set E. The local antimagic total labeling of G is a map from V ∪ E to the set of positive integers from 1 to |V| + |E| such that the weight of two adjacent vertices are distinct. The weight of a vertex v is calculated by the sum of the label of the vertex v and the labels of all edges incident to it. If the vertices of G is labelled by the smallest labels, that is, {1, 2,…, |V|}, then the such labeling is called local super antimagic total labeling. Thus, the local super antimagic total labeling induces a proper vertex coloring of G where the vertex v is colored by the weight of vertex v. The minimum number of colors taken over all colorings induced by super local antimagic total labeling of G, is called local super antimagic total chromatic number of graph G, and denoted by χlsat (G). In this paper, we consider the local super antimagic total chromatic number of some wheel related graphs such as fans, even gear graphs, and sun flower graphs.