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.