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Paired-domination number of a graph and its complement

Favaron, O ; Sharif University of Technology | 2008

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  1. Type of Document: Article
  2. DOI: 10.1016/j.disc.2007.11.034
  3. Publisher: 2008
  4. Abstract:
  5. A paired-dominating set of a graph G = (V, E) with no isolated vertex is a dominating set of vertices inducing a graph with a perfect matching. The paired-domination number of G, denoted by γp r (G), is the minimum cardinality of a paired-dominating set of G. We consider graphs of order n ≥ 6, minimum degree δ such that G and over(G, -) do not have an isolated vertex and we prove that. -if γp r (G) > 4 and γp r (over(G, -)) > 4, then γp r (G) + γp r (over(G, -)) ≤ 3 + min {δ (G), δ (over(G, -))}. -if δ (G) ≥ 2 and δ (over(G, -)) ≥ 2, then γp r (G) + γp r (over(G, -)) ≤ frac(2 n, 3) + 4 and γp r (G) + γp r (over(G, -)) ≤ frac(2 n, 3) + 2 if moreover n ≥ 21. © 2007 Elsevier B.V. All rights reserved
  6. Keywords:
  7. Cardinality ; Dominating sets ; Domination numbers ; Graph g ; Isolated vertices ; Minimum degrees ; Nordhaus-Gaddum inequalities ; Paired-domination number ; Perfect matching ; Graph theory
  8. Source: Discrete Mathematics ; Volume 308, Issue 24 , 2008 , Pages 6601-6605 ; 0012365X (ISSN)
  9. URL: https://aip.scitation.org/journal/jcp