Please use this identifier to cite or link to this item: http://hdl.handle.net/10646/3381
 Title: Average distance and edge-connectivity I Authors: Dankelmann, PeterMukwembi, SimonSwart, Henda C metadata.dc.contributor.authoremail: simonmukwembi@gmail.com metadata.dc.type: Article Keywords: Plesnikverticesof G Issue Date: 15-Jan-2015 Publisher: Society for Industrial and Applied Mathematics Citation: Dankelmann, P., Mukwembi, S., & Swart, H. C. (2008). Average distance and edge-connectivity I. SIAM Journal on Discrete Mathematics, 22 (1), 92-101. 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 Description: The results in this paper are part of the second author’s PhD thesis. URI: http://hdl.handle.net/10646/3381 ISSN: 1095-7200 Appears in Collections: Department of Mathematics Staff Publications

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