Average distance, radius and remoteness of a graph

Baoyindureng Wu, Wanping Zhang

Abstract


Let G = (V, E) be a connected graph on n vertices. Denote by l-(G) the average distance between all pairs of vertices in G. The remoteness ρ(G) of a connected graph G is the maximum average distance from a vertex of G to all others. The aim of this paper is to show that two conjectures in [1] concerned with average distance, radius and remoteness of a graph are true.

[1] M. Aouchiche and P. Hansen, Proximity and remoteness in graphs: results and conjectures, Networks 58 (2011), 95–102.


Keywords


Distance, radius, eccentricity, proximity, remoteness.

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DOI: https://doi.org/10.26493/1855-3974.312.679

ISSN: 1855-3974

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