Total colorings of some classes of four regular circulant graphs

Abstract

AbstractThe total chromatic number, [Formula: see text] is the minimum number of colors which need to be assigned to obtain a total coloring of the graph G. The Total Coloring Conjecture (TCC) made independently by Behzad and Vizing that for any graph, [Formula: see text] where [Formula: see text] represents the maximum degree of G. In this paper we obtained the total chromatic number for some classes of four regular circulant graphs.

Keywords

• Total coloring
• circulant graphs
• 05C15 (primary)
• 05b15 (secondary)