Czechoslovak Mathematical Journal, Vol. 62, No. 4, pp. 1003-1009, 2012

Convex domination in the composition and
Cartesian product of graphs

Mhelmar A. Labendia, Sergio R. Canoy, Jr.

Mhelmar A. Labendia, Sergio R. Canoy, Jr., Department of Mathematics, College of Science and Mathematics, Mindanao State University - Iligan Institute of Technology, 9200 Iligan City, Philippines, e-mail: mhelmar.labendia@g.msuiit.edu.ph, e-mail: serge_canoy@yahoo.com

Abstract: In this paper we characterize the convex dominating sets in the composition and Cartesian product of two connected graphs. The concepts of clique dominating set and clique domination number of a graph are defined. It is shown that the convex domination number of a composition $G[H]$ of two non-complete connected graphs $G$ and $H$ is equal to the clique domination number of $G$. The convex domination number of the Cartesian product of two connected graphs is related to the convex domination numbers of the graphs involved.

Keywords: convex dominating set, convex domination number, clique dominating set, composition, Cartesian product

Classification (MSC 2010): 05C69


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