## 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 ofGis 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.

Original language | English |
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Pages (from-to) | 339-346 |

Number of pages | 8 |

Journal | Journal of Combinatorial Optimization |

Volume | 24 |

Issue number | 3 |

DOIs | |

Publication status | Published - Oct 2012 |

## Keywords

- Cross product
- K-tuple total domination
- Total domination

## ASJC Scopus subject areas

- Computer Science Applications
- Discrete Mathematics and Combinatorics
- Control and Optimization
- Computational Theory and Mathematics
- Applied Mathematics