Color class dominations sets in various classes of graphs
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Abstract
Let $G=(V, E)$ be a graph. A color class dominating set of $G$ is a proper coloring $\mathscr{C}$ of $G$ with the extra property that every color class in $\mathscr{C}$ is dominated by a vertex in $G$. A color class dominating set is said to be a minimal color class dominating set if no proper subset of $\mathscr{C}$ is a color class dominating set of $G$. The color class domination number of $G$ is the minimum cardinality taken over all minimal color class dominating sets of $G$ and is denoted by $\gamma_\chi(G)$. Here we also obtain $\gamma_\chi(G)$ for Multi-star graph, Windmill graph, Barbell graph, Lollipop graph, Complete m-partite graph, Fan graph, Crown graph and Cocktail party graph.
Keywords:
Chromatic number, domination number, color class dominating set, color class domination numberMathematics Subject Classification:
Mathematics- Pages: 195-198
- Date Published: 01-01-2021
- Vol. 9 No. 01 (2021): Malaya Journal of Matematik (MJM)
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Terasa W. Haynes, Stephen T. Hedetniemi, Peter J Slater, Domination in Graphs, Marcel Dekker, New york, 1998.
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