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# Average distance and edge-connectivity I

 dc.contributor.author Dankelmann, Peter dc.contributor.author Mukwembi, Simon dc.contributor.author Swart, Henda C dc.date.accessioned 2017-09-06T07:43:37Z dc.date.available 2017-09-06T07:43:37Z dc.date.issued 2015-01-15 dc.identifier.citation Dankelmann, P., Mukwembi, S., & Swart, H. C. (2008). Average distance and edge-connectivity I. SIAM Journal on Discrete Mathematics, 22 (1), 92-101. en_US dc.identifier.issn 1095-7200 dc.identifier.uri http://hdl.handle.net/10646/3381 dc.description The results in this paper are part of the second author’s PhD thesis. en_US dc.description.abstract The average distance $\mu(G)$ of a connected graph G of order n is the average of the distances between all pairs of vertices of G. We prove that if G is a $\lambda$-edge-connected graph of order n, then the bounds $\mu(G) \le 2n/15+9$ if $\lambda=5,6$, $\mu(G) \le n/9+10$ if $\lambda=7$, and $\mu(G) \le n/(\lambda+1)+5$ if $\lambda \ge 8$ hold. Our bounds are shown to be best possible, and our results solve a problem of Plesník en_US dc.description.sponsorship National Research Foundation and the University of KwaZulu-Natal en_US dc.language.iso en_ZW en_US dc.publisher Society for Industrial and Applied Mathematics en_US dc.subject Plesnik en_US dc.subject verticesof G en_US dc.title Average distance and edge-connectivity I en_US dc.type Article en_US dc.contributor.authoremail simonmukwembi@gmail.com en_US
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