Dominator coloring of Quadrilateral Snake, Triangle Snake graph and Barbell graph

Abstract

A graph G is said to have a dominator coloring if it has a proper coloring in which every vertex of the graph dominates all vertices of atleast one color class. The dominator chromatic number Xd (G) is the least number of colors required for a dominator coloring of G. The dominator chromatic number for Quadrilateral Snake graph, Triangle Snake graph and Barbell graph are derived and also the relationship between chromatic number, domination number and dominator chromatic number of these graphs are shown in this paper.