## Average distance and edge-connectivity I

##### Date

2015-01-15##### Author

Dankelmann, Peter

Mukwembi, Simon

Swart, Henda C

##### Type

Article##### Metadata

Show full item record##### 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

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**Additional Citation Information**

Dankelmann, P., Mukwembi, S., & Swart, H. C. (2008). Average distance and edge-connectivity I. SIAM Journal on Discrete Mathematics, 22 (1), 92-101.#####
**Sponsor**

National Research Foundation and the University of KwaZulu-Natal#####
**Publisher**

Society for Industrial and Applied Mathematics

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**Additional Notes**

The results in this paper are part of the second author’s PhD thesis.