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  • Giudici, Michael; Verret, Gabriel

    arXiv (Cornell University), 01/2019
    Paper, Journal Article

    We prove that every finite arc-transitive graph of valency twice a prime admits a nontrivial semiregular automorphism, that is, a non-identity automorphism whose cycles all have the same length. This is a special case of the Polycirculant Conjecture, which states that all finite vertex-transitive digraphs admit such automorphisms.