k-tuple total domination in cross products of graphs

  • Authors:

  • Michael A. Henning;Adel P. Kazemi

  • Affiliations:

  • Department of Mathematics, University of Johannesburg, Auckland Park, South Africa 2006;Department of Mathematics, University of Mohaghegh Ardabili, Ardabil, Iran

  • Venue:
  • Journal of Combinatorial Optimization
  • Year:
  • 2012

Quantified Score

Hi-index 0.00

Visualization

Abstract

For k驴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脳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.