Paired-domination in generalized claw-free graphs

Paul Dorbec, Sylvain Gravier, Michael A. Henning

Research output: Contribution to journalArticlepeer-review

36 Citations (Scopus)


In this paper, we continue the study of paired-domination in graphs introduced by Haynes and Slater (Networks 32 (1998) 199-206). A set S of vertices in a graph G is a paired-dominating set of G if every vertex of G is adjacent to some vertex in S and if the subgraph induced by S contains a perfect matching. The paired-domination number of G, denoted by γpr(G) , is the minimum cardinality of a paired-dominating set of G. If G does not contain a graph F as an induced subgraph, then G is said to be F-free. Haynes and Slater (Networks 32 (1998) 199-206) showed that if G is a connected graph of order n ≥ 3, then γpr(G) ≤ n-1 and this bound is sharp for graphs of arbitrarily large order. Every graph is K1,a+2-free for some integer a ≥ 0. We show that for every integer a ≥ 0, if G is a connected K1,a+2-free graph of order n ≥ 2, then γpr(G) ≤ 2(an + 1)/(2a+1) with infinitely many extremal graphs.

Original languageEnglish
Pages (from-to)1-7
Number of pages7
JournalJournal of Combinatorial Optimization
Issue number1
Publication statusPublished - Jul 2007
Externally publishedYes


  • Bounds
  • Generalized claw-free graphs
  • Paired-domination

ASJC Scopus subject areas

  • Computer Science Applications
  • Discrete Mathematics and Combinatorics
  • Control and Optimization
  • Computational Theory and Mathematics
  • Applied Mathematics


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