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}
}