## Abstract

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 γ_{pr}(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 γ_{pr}(G) ≤ n-1 and this bound is sharp for graphs of arbitrarily large order. Every graph is K_{1,a+2}-free for some integer a ≥ 0. We show that for every integer a ≥ 0, if G is a connected K_{1,a+2}-free graph of order n ≥ 2, then γ_{pr}(G) ≤ 2(an + 1)/(2a+1) with infinitely many extremal graphs.

Original language | English |
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Pages (from-to) | 1-7 |

Number of pages | 7 |

Journal | Journal of Combinatorial Optimization |

Volume | 14 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jul 2007 |

Externally published | Yes |

## Keywords

- 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