# On the dominated chromatic number of certain graphs

Document Type : Research Paper

Authors

Department of Mathematics, Yazd University, 89195-741, Yazd, Iran

10.22108/toc.2020.119361.1675

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.

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