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