Approaches that output infinitely many graphs with small local antimagic chromatic number

Abstract

An edge labeling of a connected 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 x and y, [Formula: see text], where the induced vertex label [Formula: see text], with e ranging over all the edges incident to x. The local antimagic chromatic number of G, denoted by [Formula: see text], is the minimum number of distinct induced vertex labels over all local antimagic labelings of G. In this paper, we show the existence of infinitely many bipartite and tripartite graphs with [Formula: see text].