Locally identifying coloring in some chordal graphs

Abstract

A locally identifying coloring (or lid-coloring for short) in a graph is a proper vertex coloring such that, for any edge uv, if u and v have distinct closed neighborhoods, then the set of colors used on vertices of the closed neighborhoods of u and v are distinct.The lid-chromatic number of a graph G, denoted by χ lid (G), is the minimum number of colors needed in any lid-coloring of G.In this work, we determine the lid-chromatic number of subclasses of both powers of paths and some split graphs, which are chordal graphs.Additionally, we present a lower bound for the lid-chromatic number in twin-free graphs.