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 $\chi_{dom}(G)$...
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| Published in | Transactions on combinatorics Vol. 9; no. 4; pp. 217 - 230 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
University of Isfahan
01.12.2020
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| Subjects | |
| Online Access | Get full text |
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| Summary: | 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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| ISSN: | 2251-8657 2251-8665 |
| DOI: | 10.22108/toc.2020.119361.1675 |