发表机构
Amrita Vishwa Vidyapeetham, Coimbatore Tamil Nadu, India（印度泰米尔纳德邦哥印拜陀阿弥塔大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文刻画了色支配的完美图，并研究了几类无圈图的支配色数，为图染色理论提供了新结果。
AI 中文摘要
图$G$的支配染色是一种适当的顶点染色，使得每个颜色类都被一个顶点所支配。图$G$的支配染色所需的最少颜色数称为图$G$的支配色数，记为$\chi_{dom}(G)$。若$\chi(G)=\chi_{dom}(G)$，则称图$G$是色支配的。在本文中，我们刻画了哪些完美图是色支配的。此外，我们还研究了几类无圈图的支配色数。
英文摘要
The dominated coloring of a graph $G$ is a proper vertex coloring such that each color class is dominated by a vertex. The minimum number of colors required for a dominated coloring of a graph $G$ is called the dominated chromatic number of the graph $G$ and is denoted by $χ_{dom}(G)$. A graph $G$ is said to be chromatic dominated if $χ(G)=χ_{dom}(G)$. In this paper, we characterized the perfect graphs, which are chromatic dominated. Also, we studied the dominated chromatic number of some classes of unicyclic graphs.
