On the dominated chromatic number of certain graphs

Let G be a simple graph. The dominated coloring of 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 χdom(G). Stability (bondage number) of dominated chromatic number of G is the minimum number of vertices (edges) of G whose removal changes the dominated chromatic number of G. In this paper, we study the dominated chromatic number, dominated stability and dominated bondage number of certain graphs.