Dominated chromatic number of some operations on a graph

Abstract

Let $G$ be a simple graph. The dominated coloring of a graph $G$ is a proper coloring of $G$ such that each color class is dominated by at least one vertex. The minimum number of colors needed for a dominated coloring of $G$ is called the dominated chromatic number of $G$, denoted by $\chi_{dom}(G)$. In this paper, we examine the effects on $\chi_{dom}(G)$ when $G$ is modified by operations on vertex and edge of $G$.