Geodesic
Arc-transitive graphs of valency 8 have a semiregular automorphism
Ars Mathematica Contemporanea, Tome 8 (2015) no. 1, pp. 29-34.

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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.
DOI : 10.26493/1855-3974.492.37d
Keywords: Arc-transitive graphs, polycirculant conjecture, semiregular automorphism 
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Gabriel Verret. Arc-transitive graphs of valency 8 have a semiregular automorphism. Ars Mathematica Contemporanea, Tome 8 (2015) no. 1, pp. 29-34. doi : 10.26493/1855-3974.492.37d. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.492.37d/

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