Convex domination in the composition and cartesian product of graphs
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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 productMSC 2010
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© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2012