Arc-transitive graphs of valency twice a prime admit a semiregular automorphism

Gabriel Verret

Abstract


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.


Keywords


Arc-transitive graphs; polycirculant conjecture; semiregular automorphism

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ISSN: 1855-3974

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