k-tuple total domination in cross products of graphs

Michael A. Henning () and Adel P. Kazemi ()
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Michael A. Henning: University of Johannesburg
Adel P. Kazemi: University of Mohaghegh Ardabili

Journal of Combinatorial Optimization, 2012, vol. 24, issue 3, No 13, 339-346

Abstract: 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.

Keywords: Cross product; Total domination; k-tuple total domination (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/s10878-011-9389-z

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