University of IsfahanTransactions on Combinatorics2251-86579420201201On the dominated chromatic number of certain graphs2172302486210.22108/toc.2020.119361.1675ENSaeidAlikhaniDepartment of Mathematics, Yazd University, 89195-741, Yazd, IranMohammad RezaPiriDepartment of Mathematics, Yazd University, 89195-741, Yazd, IranJournal Article20190925Let $G$ 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.
https://toc.ui.ac.ir/article_24862_7ee6f29ca5ca8795e3a390c8fe8145c4.pdf