Semiregular automorphisms of edge-transitive graphs
Combinatorics
2013-06-11 v1 Group Theory
Abstract
The polycirculant conjecture asserts that every vertex-transitive digraph has a semiregular automorphism, that is, a nontrivial automorphism whose cycles all have the same length. In this paper we investigate the existence of semiregular automorphisms of edge-transitive graphs. In particular, we show that any regular edge-transitive graph of valency three or four has a semiregular automorphism.
Keywords
Cite
@article{arxiv.1306.1971,
title = {Semiregular automorphisms of edge-transitive graphs},
author = {Michael Giudici and Primoz Potocnik and Gabriel Verret},
journal= {arXiv preprint arXiv:1306.1971},
year = {2013}
}