Domination and dominator coloring of neighborhood corona of certain graphs

Abstract

A dominator coloring of a graph G is a proper coloring of G in which each vertex of the graph dominates every vertex of some color class. The dominator chromatic number of G is the minimum number of color classes in a dominator coloring of G. When operation on graphs is performed on classes of graphs result from the new class of graphs are obtained. The neighborhood corona is one such operation on graphs, having interesting applications as well. In this paper we study this operation on certain graph classes and discuss the bounds in terms of domination number and dominator chromatic number.