On the Equitable Total Coloring of Multiple Join-Graph

Abstract:

      A total-coloring is called equitable if $| \mid S_{i}\mid-\mid S_{j}\mid |\leq 1$, where $\mid S_{i}\mid$ is the chromatic number of the color. The minimum number of colors required for an equitable proper total-coloring. A simple graph $G$ is denoted by $\chi_{et}(G)$. In this paper, we prove theorems of equitable total coloring of multiple join-graph and get equitable total chromatic numbers of some special multiple join-graph.