Elsevier

Discrete Applied Mathematics

Volume 174, 10 September 2014, Pages 81-91
Discrete Applied Mathematics

On the algorithmic complexity of k-tuple total domination

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Abstract

For a fixed positive integer k, a k-tuple total dominating set of a graph G is a set DV(G) such that every vertex of G is adjacent to at least k vertices in D. The k-tuple total domination problem is to determine a minimum k-tuple total dominating set of G. This paper studies k-tuple total domination from an algorithmic point of view. In particular, we present a linear-time algorithm for the k-tuple total domination problem for graphs in which each block is a clique, a cycle or a complete bipartite graph, which include trees, block graphs, cacti and block-cactus graphs. We also establish NP-hardness of the k-tuple total domination problem in undirected path graphs.

Keywords

k-tuple total domination
Total domination
Block graph
Cactus
Algorithm
NP-complete
Undirected path graph

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This research was partially supported by the National Science Council of the Republic of China under grants NSC100-2811-M-002-146 and NSC101-2115-M-002-005-MY3.