Total domination coloring of graphs

Abstract

A total domination coloring of a graph G is a proper coloring of G in which open neighbourhood of each vertex contains at least one color class and each color class is dominated by at least one vertex. The minimum number of colors required for a total domination coloring of G is called the total domination chromatic number of G and is denoted by χtd(G). In this paper, we study the total domination chromatic number of some graph classes. The bounds of total domination chromatic number with respect to the graph parameters such as the domination number, chromatic number, total dominator chromatic number and total domination number are also studied.