Mean distance in a graph

J. K. Doyle; J. E. Graver

doi:10.1016/0012-365X(77)90144-3

Mean distance in a graph

J. K. Doyle, J. E. Graver

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

110 Scopus citations

Abstract

The average or mean of the distances between vertices in a connected graph Γ, μ(Γ), is a natural measure of the compactness of the graph. In this paper we compute bounds for μ(Γ) in terms of the number of vertices in Γ and the diameter of Γ. We prove a formula for computing μ(Γ) when Γ is a tree which is particularly useful when Γ has a high degree of symmetry. Finally, we present algorithms for μ(Γ) which are amenable to computer implementation.

Original language	English (US)
Pages (from-to)	147-154
Number of pages	8
Journal	Discrete Mathematics
Volume	17
Issue number	2
DOIs	https://doi.org/10.1016/0012-365X(77)90144-3
State	Published - 1977

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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10.1016/0012-365X(77)90144-3

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AB - The average or mean of the distances between vertices in a connected graph Γ, μ(Γ), is a natural measure of the compactness of the graph. In this paper we compute bounds for μ(Γ) in terms of the number of vertices in Γ and the diameter of Γ. We prove a formula for computing μ(Γ) when Γ is a tree which is particularly useful when Γ has a high degree of symmetry. Finally, we present algorithms for μ(Γ) which are amenable to computer implementation.

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Mean distance in a graph

Abstract

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