Locally identifying coloring of corona product of graphs

Abstract

A proper vertex coloring of a graph [Formula: see text] is said to be locally identifying (lid-coloring) if for any pair [Formula: see text] of adjacent vertices with distinct closed neighborhoods, the sets of colors in the closed neighborhoods of [Formula: see text] and [Formula: see text] are different. The smallest integer [Formula: see text] for which [Formula: see text] admits a lid-coloring is called the lid-chromatic number of [Formula: see text]. The corona product [Formula: see text] of two graphs [Formula: see text] and [Formula: see text] is the graph obtained by taking one copy of [Formula: see text] and [Formula: see text] copies of [Formula: see text], and then joining the [Formula: see text]th vertex of [Formula: see text] to every vertex in the [Formula: see text]th copy of [Formula: see text] for every [Formula: see text], where [Formula: see text] denotes the number of elements in the set [Formula: see text]. In this paper, the lid-chromatic number of corona product of graphs has been studied.