Average distance and edge-connectivity II

Peter Dankelmann; Simon Mukwembi; Henda C. Swart

doi:10.1137/06065653X

Average distance and edge-connectivity II

Peter Dankelmann
, Simon Mukwembi
, Henda C. Swart

University of KwaZulu-Natal

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

14 Citations (Scopus)

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. We prove that for a 3-edge-connected graph G of order n the inequality μ(G) ≤ n/6 + 24 on the average distance holds. Our bound is shown to be best possible even if G is 4-edge-connected, and our results answer, in part, a question of Plesník [J. Graph Theory, 8 (1984), pp. 1-24].

Original language	English
Pages (from-to)	1035-1052
Number of pages	18
Journal	SIAM Journal on Discrete Mathematics
Volume	21
Issue number	4
DOIs	https://doi.org/10.1137/06065653X
Publication status	Published - 2007
Externally published	Yes

Keywords

Average distance
Distance
Edge-connectivity

ASJC Scopus subject areas

General Mathematics

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10.1137/06065653X

Cite this

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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. We prove that for a 3-edge-connected graph G of order n the inequality μ(G) ≤ n/6 + 24 on the average distance holds. Our bound is shown to be best possible even if G is 4-edge-connected, and our results answer, in part, a question of Plesn{\'i}k [J. Graph Theory, 8 (1984), pp. 1-24].",

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KW - Distance

KW - Edge-connectivity

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Average distance and edge-connectivity II

Abstract

Keywords

ASJC Scopus subject areas

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