## Abstract

Let G be a finite, connected graph. The average distance of a vertex v of G is the arithmetic mean of the distances from v to all other vertices of G. The remoteness ρ(G) and the proximity π(G) of G are the maximum and the minimum of the average distances of the vertices of G. In this paper, we present a sharp upper bound on the remoteness of a triangle-free graph of given order and minimum degree, and a corresponding bound on the proximity, which is sharp apart from an additive constant. We also present upper bounds on the remoteness and proximity of C_{4}-free graphs of given order and minimum degree, and we demonstrate that these are close to being best possible.

Original language | English |
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Article number | 112513 |

Journal | Discrete Mathematics |

Volume | 344 |

Issue number | 9 |

DOIs | |

Publication status | Published - Sept 2021 |

## Keywords

- Average distance
- Distance
- Distance in graphs
- Minimum degree
- Proximity
- Remoteness

## ASJC Scopus subject areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics

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