Power Dominator Chromatic Number for vertex duplication of some Graphs

Abstract

Let G = (V, E) be a finite, undirected and connected graph without loops and multiple edges. Then the power dominator coloring of G is a proper coloring, such that each vertex of G power dominates every vertex of some color class. The least number of color classes in a power dominator coloring of the graph, is the power dominator chromatic number . In this paper, we find the Power Dominator Chromatic Number for some graphs such as Path, Cycle, Complete Graph, Bipartite Graph, Double fan Graph, Octopus Graph and Venessa Graph, with the context of vertex duplication.