On geodesic transitive graphs

W. Jin, Alice Devillers, Cai-Heng Li, Cheryl Praeger

    Research output: Contribution to journalArticlepeer-review

    14 Citations (Web of Science)


    © 2014 Elsevier B.V. All rights reserved. The main purpose of this paper is to investigate relationships between three graph symmetry properties: s-arc transitivity, s-geodesic transitivity, and s-distance transitivity. A well-known result of Weiss tells us that if a graph of valency at least 3 is s-arc transitive then s≤7. We show that for each value of s≤3, there are infinitely many s-arc transitive graphs that are t-geodesic transitive for arbitrarily large values of t. For 4≤s≤7, the geodesic transitive graphs that are s-arc transitive can be explicitly described, and all but two of these graphs are related to classical generalized polygons. Finally, we show that the Paley graphs and the Peisert graphs, which are known to be distance transitive, are almost never 2-geodesic transitive, with just three small exceptions.
    Original languageEnglish
    Pages (from-to)168-173
    Number of pages6
    JournalDiscrete Mathematics
    Issue number3
    Publication statusPublished - 6 Mar 2015


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