English

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

Combinatorics 2019-01-03 v1

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

Cite

@article{arxiv.1901.00084,
  title  = {Arc-transitive graphs of valency twice a prime admit a semiregular automorphism},
  author = {Michael Giudici and Gabriel Verret},
  journal= {arXiv preprint arXiv:1901.00084},
  year   = {2019}
}