### Abstract

We prove the following theorems: (i) Let G be a graph and let x be a locally 2n-connected vertex. Let {u,v} be a pair of vertices in V(G) - {x} such that uv ∉ E(G), x ∈ N_{G}(u) ∩ N_{G}(v), and N_{G}(x) ⊂ N_{G}(u) ∪ N_{G}(v) ∪ {u, v}. Then if G + uv is n-extendable, then G is n-extendable or G is a member of the exceptional family F of graphs described. (ii) Let G be a (2n + l)-connected graph. Let {u,v,x} be a three-vertex subset of V(G) such that uv ∉ E(G), x ∈ N_{G}(u) ∩ N_{G}(v), and N_{G}(x) ⊂ N_{G}(u) ∪ N_{G}(v) ∪ {u,v}. If G + uv is n-extendable, then G is n-extendable or G is a member of the exceptional family F of graphs described.

Original language | English |
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Pages (from-to) | 171-175 |

Number of pages | 5 |

Journal | Australasian Journal of Combinatorics |

Volume | 32 |

Publication status | Published - 2005 Dec 1 |

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics

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## Cite this

Nishimura, T. (2005). Note on a closure concept and matching extension.

*Australasian Journal of Combinatorics*,*32*, 171-175.