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Keywords:
convex dominating set; convex domination number; clique dominating set; composition; Cartesian product
convex dominating set; convex domination number; clique dominating set; composition; Cartesian product
Summary:
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.
References:
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