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 number

Mathematics Subject Classification:

Mathematics
  • A. Vijayalekshmi Department of Mathematics, S.T.Hindu College, Nagercoil-629 002, Tamil Nadu, India.
  • A. E. Prabha Department of Mathematics, S.T.Hindu College, Nagercoil-629 002, Tamil Nadu, India.
  • Pages: 195-198
  • Date Published: 01-01-2021
  • Vol. 9 No. 01 (2021): Malaya Journal of Matematik (MJM)

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A. Vijayalekshmi, A. E. Prabha, Introduction of Color Class Dominating Sets in Graphs [Accepted].

R. M. Gera, On Dominator Colorings in Graphs, New York, Network Academy of Sciences, 2007.

F. Harrary, Graph Theory, Addition-Wesley Reading Mass, 1969.

Terasa W. Haynes, Stephen T. Hedetniemi, Peter J Slater, Domination in Graphs, Marcel Dekker, New york, 1998.

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Published

01-01-2021

How to Cite

A. Vijayalekshmi, and A. E. Prabha. “Color Class Dominations Sets in Various Classes of Graphs”. Malaya Journal of Matematik, vol. 9, no. 01, Jan. 2021, pp. 195-8, https://www.malayajournal.org/index.php/mjm/article/view/1001.