## Abstract

The average distance μ(G) of a connected graph G of order n is the average of the distances between all pairs of vertices of G, i.e., μ(G) = (^{n}_{2})^{-1} σ_{{x,y}⊂}V(G) d _{g}(x,y), where V(G) denotes the vertex set of G and d_{G}(x, y) is the distance between x and y. We prove that if G is a κ-vertex- connected graph, κ≥3 an odd integer, of order n, then μ(G)≤ n/2(κ+1) + O(1). Our bound is shown to be best possible and our results, apart from answering a question of Plesník [J Graph Theory 8 (1984), 1-24], Favaron et al. [Networks 19 (1989), 493-504], can be used to deduce a theorem that is essentially equivalent to a theorem by Egawa and Inoue [Ars Combin 51 (1999), 89-95] on the radius of a κ-vertex-connected graph of given order, where κ is odd.

Original language | English |
---|---|

Pages (from-to) | 157-177 |

Number of pages | 21 |

Journal | Journal of Graph Theory |

Volume | 62 |

Issue number | 2 |

DOIs | |

Publication status | Published - Oct 2009 |

Externally published | Yes |

## Keywords

- Average distance
- Connectivity
- Distance
- Radius

## ASJC Scopus subject areas

- Geometry and Topology