Semiregular automorphisms in vertex-transitive graphs with a solvable group of automorphisms
Ars Mathematica Contemporanea, Tome 13 (2017) no. 2, pp. 461-468.

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It has been conjectured that automorphism groups of vertex-transitive (di)graphs, and more generally 2-closures of transitive permutation groups, must necessarily possess a fixed-point-free element of prime order, and thus a non-identity element with all orbits of the same length, in other words, a semiregular element. The known affirmative answers for graphs with primitive and quasiprimitive groups of automorphisms suggest that solvable groups need to be considered if one is to hope for a complete solution of this conjecture. It is the purpose of this paper to present an overview of known results and suggest possible further lines of research towards a complete solution of the problem.
DOI : 10.26493/1855-3974.1486.a33
Keywords: Solvable group, semiregular automorphism, fixed-point-free automorphism, polycirculant conjecture
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Dragan Marušič. Semiregular automorphisms in vertex-transitive graphs with a solvable group of automorphisms. Ars Mathematica Contemporanea, Tome 13 (2017) no. 2, pp. 461-468. doi : 10.26493/1855-3974.1486.a33. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.1486.a33/

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