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k-tuple total domination in cross products of graphs

Author

Listed:
  • Michael A. Henning

    (University of Johannesburg)

  • Adel P. Kazemi

    (University of Mohaghegh Ardabili)

Abstract

For k≥1 an integer, a set S of vertices in a graph G with minimum degree at least k is a k-tuple total dominating set of G if every vertex of G is adjacent to at least k vertices in S. The minimum cardinality of a k-tuple total dominating set of G is the k-tuple total domination number of G. When k=1, the k-tuple total domination number is the well-studied total domination number. In this paper, we establish upper and lower bounds on the k-tuple total domination number of the cross product graph G×H for any two graphs G and H with minimum degree at least k. In particular, we determine the exact value of the k-tuple total domination number of the cross product of two complete graphs.

Suggested Citation

  • Michael A. Henning & Adel P. Kazemi, 2012. "k-tuple total domination in cross products of graphs," Journal of Combinatorial Optimization, Springer, vol. 24(3), pages 339-346, October.
    • Handle: RePEc:spr:jcomop:v:24:y:2012:i:3:d:10.1007_s10878-011-9389-z
    DOI: 10.1007/s10878-011-9389-z
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