Semiregular automorphisms in vertex-transitive graphs with a solvable group of automorphismsMarušič, Dragan (Avtor) solvable groupsemiregular automorphismfixed-point-free automorphismpolycirculant conjectureIt 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.20172022-01-03 01:14:36Neznano17629UDK: 519.17:512.54ISSN pri članku: 1855-3966COBISS.SI-ID: 1539752900sl