Arc-transitive graphs of valency twice a prime admit a semiregular automorphism - Giudici, Michael (Ars mathematica contemporanea, 2020)
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; ločno tranzitivni grafi; policirkulantna domneva; polycirculant conjecture; semiregular automorphism; semiregularni avtomorfizem