Information Processing Letters
Journal of Graph Theory
FCT'11 Proceedings of the 18th international conference on Fundamentals of computation theory
Strong Transversals in Hypergraphs and Double Total Domination in Graphs
SIAM Journal on Discrete Mathematics
Algorithmic aspects of k-tuple total domination in graphs
Information Processing Letters
k-tuple total domination in cross products of graphs
Journal of Combinatorial Optimization
On the approximability and exact algorithms for vector domination and related problems in graphs
Discrete Applied Mathematics
Note: On upper bounds for multiple domination numbers of graphs
Discrete Applied Mathematics
Hardness results and approximation algorithm for total liar's domination in graphs
Journal of Combinatorial Optimization
Efficient self-stabilizing algorithms for minimal total k-dominating sets in graphs
Information Processing Letters
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A set S of vertices in a graph G is a k-tuple total dominating set, abbreviated kTDS, of G if every vertex of G is adjacent to least k vertices in S. The minimum cardinality of a kTDS of G is the k-tuple total domination number of G. For a graph to have a kTDS, its minimum degree is at least k. When k=1, a k-tuple total domination number is the well-studied total domination number. When k=2, a kTDS is called a double total dominating set and the k-tuple total domination number is called the double total domination number. We present properties of minimal kTDS and show that the problem of finding kTDSs in graphs can be translated to the problem of finding k-transversals in hypergraphs. We investigate the k-tuple total domination number for complete multipartite graphs. Upper bounds on the k-tuple total domination number of general graphs are presented.