Arc-transitive graphs of valency 8 have a semiregular automorphism

Gabriel Verret

Abstract


One version of the polycirculant conjecture states that every vertex-transitive graph has a non-identity semiregular automorphism that is, a non-identity automorphism whose cycles all have the same length.  We give a proof of the conjecture in the arc-transitive case for graphs of valency 8, which was the smallest open valency.

Keywords


Arc-transitive graphs, polycirculant conjecture, semiregular automorphism

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DOI: https://doi.org/10.26493/1855-3974.492.37d

ISSN: 1855-3974

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