Upper k-tuple domination in graphs - Archive ouverte HAL
Journal Articles Discrete Mathematics and Theoretical Computer Science Year : 2012

Upper k-tuple domination in graphs

Abstract

For a positive integer k, a k-tuple dominating set of a graph G is a subset S of V (G) such that |N [v] ∩ S| ≥ k for every vertex v, where N [v] = {v} ∪ {u ∈ V (G) : uv ∈ E(G)}. The upper k-tuple domination number of G, denoted by Γ×k (G), is the maximum cardinality of a minimal k-tuple dominating set of G. In this paper we present an upper bound on Γ×k (G) for r-regular graphs G with r ≥ k, and characterize extremal graphs achieving the upper bound. We also establish an upper bound on Γ×2 (G) for claw-free r-regular graphs. For the algorithmic aspect, we show that the upper k-tuple domination problem is NP-complete for bipartite graphs and for chordal graphs.
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Dates and versions

hal-00903694 , version 1 (04-06-2014)

Identifiers

Cite

Gerard Jennhwa Chang, Paul Dorbec, Hye Kyung Kim, André Raspaud, Haichao Wang, et al.. Upper k-tuple domination in graphs. Discrete Mathematics and Theoretical Computer Science, 2012, Vol. 14 no. 2 (2), pp.285-292. ⟨10.46298/dmtcs.593⟩. ⟨hal-00903694⟩

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