Total Colorings of Some Classes of FourRegular Circulant Graphs

Abstract

The total chromatic number, $\ddot{I}{‡}^{\prime \prime }(G)$ 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, $\ddot{I}{‡}^{\prime \prime }(G)\le \hat{I}”(G)+2$, where $\hat{I}”(G)$ represents the maximum degree of $G$. In this paper we obtained the total chromatic number for some classes of four regular circulant graphs.