Total Coloring of the Prismatic Graphs Dicrete Mathematics, Algorithms & Applications

Abstract

A total coloring of a graph is an assignment of colors to all the elements of the graph such that no two adjacent or incident elements receive the same color. A graph GG is prismatic, if for every triangle TT, every vertex not in TT has exactly one neighbor in TT. In this paper, we prove the total coloring conjecture (TCC) for prismatic graphs and the tight bound of the TCC for some classes of prismatic graphs