# Average distance and edge-connectivity I

Dankelmann, Peter (2015) Average distance and edge-connectivity I.

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Official URL: http://hdl.handle.net/10646/3381

## Abstract

The results in this paper are part of the second authorâ€™s PhD thesis.,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 PlesnÃ­k,National Research Foundation and the University of KwaZulu-Natal

Item Type: Article Plesnik,verticesof G Universities > State Universities > University of Zimbabwe Mr. Edmore Sibanda 09 Sep 2017 22:01 09 Sep 2017 22:01 http://researchdatabase.ac.zw/id/eprint/5585