Finite 2-Geodesic Transitive Graphs of Prime Valency

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    Abstract

    © 2014 Wiley Periodicals, Inc. Abstract We classify noncomplete prime valency graphs satisfying the property that their automorphism group is transitive on both the set of arcs and the set of 2-geodesics. We prove that either Γ is 2-arc transitive or the valency p satisfies p≡1 (mod 4), and for each such prime there is a unique graph with this property: it is a nonbipartite antipodal double cover of the complete graph Kp+1 with automorphism group PSL(2, p) × Z2 and diameter 3.
    Original languageEnglish
    Pages (from-to)18-27
    JournalJournal of Graph Theory
    Volume80
    Issue number1
    DOIs
    Publication statusPublished - 2015

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