On the upper total domination number of Cartesian products of graphs

Paul Dorbec (), Michael A. Henning () and Douglas F. Rall ()
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Paul Dorbec: University of KwaZulu-Natal
Michael A. Henning: University of KwaZulu-Natal
Douglas F. Rall: Furman University

Journal of Combinatorial Optimization, 2008, vol. 16, issue 1, No 6, 68-80

Abstract: Abstract In this paper we continue the investigation of total domination in Cartesian products of graphs first studied in (Henning, M.A., Rall, D.F. in Graphs Comb. 21:63–69, 2005). A set S of vertices in a graph G is a total dominating set of G if every vertex in G is adjacent to some vertex in S. The maximum cardinality of a minimal total dominating set of G is the upper total domination number of G, denoted by Γ t (G). We prove that the product of the upper total domination numbers of any graphs G and H without isolated vertices is at most twice the upper total domination number of their Cartesian product; that is, Γ t (G)Γ t (H)≤2Γ t (G □ H).

Keywords: Graph products; Upper domination number; Upper total domination number (search for similar items in EconPapers)
Date: 2008
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DOI: 10.1007/s10878-007-9099-8

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