Local antimagic chromatic number of firefly graphs

Abstract

Graph labeling is one of the Graph Theory research topics that associate a graph element, such as vertices or edges, to integers called labels. There are many papers in the literature that investigate problems related to this topic. Given a connected graph G = (V, E) with at least three vertices, a local antimagic labeling is a bijection f: E -> {1, 2, ..., |E|} which induces, naturally, a labeling of vertices in G, so that adjacent vertices no admit the same label. The smaller number of vertex labels, induced by all local antimagic labels of G, is called local antimagic chromatic number of G. Since 2017, this parameter has received a lot of attention from researchers. In this article, we construct local antimagic labels for graphs belonging to the firefly graph class and provide expressions that determine the local antimagic chromatic number for all graphs in this class.