Equitable Coloring On Rooted Product Of Graphs

Abstract

A finite and simple graph is said to be equitably colorable if its vertices can be partitioned into classes such that each is an independent set and holds for every . The smallest integer for which is equitable chromatic number of and denoted by . The equitable chromatic threshold of a graph , denoted by , is the minimum such that is equitably colorable for all . This paper focuses on the equitable colorability of rooted product of graphs, in particular, exact values or upper bounds of and when and are cycles, paths, complete graphs and complete partite graphs have been found.