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: firstname.lastname@example.org, e-mail: email@example.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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