Graphs with large paired-domination number

Michael A. Henning ()
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Michael A. Henning: University of KwaZulu-Natal

Journal of Combinatorial Optimization, 2007, vol. 13, issue 1, No 5, 78 pages

Abstract: Abstract In this paper, we continue the study of paired-domination in graphs introduced by Haynes and Slater (1998) Networks 32: 199–206. A paired-dominating set of a graph G with no isolated vertex is a dominating set of vertices whose induced subgraph has a perfect matching. The paired-domination number of G, denoted by $$\gamma_{\rm pr}(G)$$ , is the minimum cardinality of a paired-dominating set of G. Let G be a connected graph of order n with minimum degree at least two. Haynes and Slater (1998) Networks 32: 199–206, showed that if n ≥ 6, then $$\gamma_{\rm pr}(G) \le 2n/3$$ . In this paper, we show that there are exactly ten graphs that achieve equality in this bound. For n ≥ 14, we show that $$\gamma_{\rm pr}(G) \le 2(n-1)/3$$ and we characterize the (infinite family of) graphs that achieve equality in this bound.

Keywords: Bounds; Paired-domination; Minimum degree two (search for similar items in EconPapers)
Date: 2007
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Citations: View citations in EconPapers (9)

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DOI: 10.1007/s10878-006-9014-8

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