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    Average distance and edge-connectivity I

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    The results in this paper are part of the second author’s PhD thesis. (305.7Kb)
    Date
    2015-01-15
    Author
    Dankelmann, Peter
    Mukwembi, Simon
    Swart, Henda C
    Type
    Article
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    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
    URI
    http://hdl.handle.net/10646/3381
    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
    Subject
    Plesnik
    verticesof G
    Additional Notes
    The results in this paper are part of the second author’s PhD thesis.
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    • Department of Mathematics Staff Publications [14]

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