The total dominator coloring of dense, octahedral and queen’s graphs

Abstract

Abstract Let G be a graph, then the dominator coloring of G is a proper coloring, in which every vertex of G dominates every vertex of at least one color class. The Total dominator coloring of graph is a proper coloring with extra property that every vertex in the graph properly dominates an entire color class. The total dominator chromatic number X d t ( G ) of G is the minimum number of color classes in a total dominator coloring of it. In this paper, total dominator coloring of dense, octahedral and queen’s graphs have been disscussed.