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On the upper total domination number of Cartesian products of graphs

Author

Listed:
  • Paul Dorbec

    (University of KwaZulu-Natal
    Institut Fourier Organization UJF-ERTé “Maths à modeler”)

  • Michael A. Henning

    (University of KwaZulu-Natal)

  • Douglas F. Rall

    (Furman University)

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).

Suggested Citation

  • Paul Dorbec & Michael A. Henning & Douglas F. Rall, 2008. "On the upper total domination number of Cartesian products of graphs," Journal of Combinatorial Optimization, Springer, vol. 16(1), pages 68-80, July.
    • Handle: RePEc:spr:jcomop:v:16:y:2008:i:1:d:10.1007_s10878-007-9099-8
    DOI: 10.1007/s10878-007-9099-8
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