On the dominated chromatic number of certain graphs

Abstract

‎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 $\chi_{dom}(G)$‎. ‎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. ‎

Keywords

• ‎dominated chromatic number
• stability
• bondage number