The Equitable Total Chromatic Number of Some Join graphs

Abstract

A proper total-coloring of graph G is said to be equitable if the number of elements (vertices and edges) in any two color classes differ by at most one, which the required minimum number of colors is called the equitable total chromatic number.In this paper, we prove some theorems on equitable total coloring and derive the equitable total chromatic numbers of Pm ∨ Sn, Pm ∨ Fn and Pm ∨ Wn.