Locally identifying coloring of strong 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 strong product [Formula: see text] of two graphs [Formula: see text] and [Formula: see text] is the graph with vertex set [Formula: see text], and two vertices [Formula: see text], [Formula: see text] are adjacent if [Formula: see text] and [Formula: see text] or [Formula: see text] and [Formula: see text] or [Formula: see text] and [Formula: see text]. In this paper, the lid-chromatic number of strong product of graphs have been studied.