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    Edge growth in graph powers

    Pokrovskiy, Alexey (2013) Edge growth in graph powers. Australasian Journal of Combinatorics 58 (2), pp. 347-357. ISSN 2202-3518.

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    Abstract

    For a graph G, its rth power G^r has the same vertex set as G, and has an edge between any two vertices within distance r of each other in G. We give a lower bound for the number of edges in the rth power of G in terms of the order of G and the minimal degree of G. As a corollary we determine how small the ratio e(G^r)/e(G) can be for regular graphs of diameter at least r.

    Metadata

    Item Type: Article
    School: School of Business, Economics & Informatics > Economics, Mathematics and Statistics
    Depositing User: Alexey Pokrovskiy
    Date Deposited: 21 Jan 2019 15:51
    Last Modified: 10 Feb 2021 21:05
    URI: https://eprints.bbk.ac.uk/id/eprint/25903

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