Total Global Dominator Coloring of Graphs

Abstract

The minimum number of colors required for the total global dominator coloring of graph is called the total global dominator chromatic number. A graph coloring is an assignment of colors to vertices or edges or both of graph. The minimum number of colors required to color the vertices of a graph such that the adjacent vertices possess different colors is known as chromatic number of graph. In the light of the above notions, a total dominator coloring of a graph can be viewed as a proper coloring in which every vertex of graph has a proper dom-color class. It is clear that all graphs which admit a total global dominator coloring also admit a global dominator coloring and every total global dominator coloring is also a global dominator coloring. The chapter provides the conditions for a graph of order to admit total global dominator coloring and the bounds. Here they also find the relationships between the parameters.