Minimum 2-tuple dominating set of permutation graphs
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- Barman, S.C., Mondal, S. & Pal, M. J. Appl. Math. Comput. (2013) 43: 133. doi:10.1007/s12190-013-0656-2
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For a fixed positive integer k, a k-tuple dominating set of a graph G=(V,E) is a subset D⊆V such that every vertex in V is dominated by at least k vertex in D. The k-tuple domination number γ×k(G) is the minimum size of a k-tuple dominating set of G. The special case when k=1 is the usual domination. The case when k=2 was called double domination or 2-tuple domination. A 2-tuple dominating set D2 is said to be minimal if there does not exist any D′⊂D2 such that D′ is a 2-tuple dominating set of G. A 2-tuple dominating set D2, denoted by γ×2(G), is said to be minimum, if it is minimal as well as it gives 2-tuple domination number. In this paper, we present an efficient algorithm to find a minimum 2-tuple dominating set on permutation graphs with n vertices which runs in O(n2) time.