On local antimagic chromatic number of cycle-related join graphs II

Abstract

An edge labeling of a graph [Formula: see text] is said to be local antimagic if it is a bijection [Formula: see text] such that for any pair of adjacent vertices [Formula: see text] and [Formula: see text], [Formula: see text], where the induced vertex label of [Formula: see text] is [Formula: see text] ([Formula: see text] is the set of edges incident to [Formula: see text]). The local antimagic chromatic number of [Formula: see text], denoted by [Formula: see text], is the minimum number of distinct induced vertex labels over all local antimagic labelings of [Formula: see text]. In this paper, several sufficient conditions to determine the local antimagic chromatic number of the join of graphs are obtained. We then determine the exact value of the local antimagic chromatic number of many join graphs.