On automorphism groups of half-arc-transitive tetravalent graphs
Group Theory
2025-12-29 v1 Combinatorics
Abstract
We characterize connected tetravalent graphs which admit groups of automorphisms such that is -half-arc-transitive and -arc-transitive. Examples for each case are constructed, including a counter-example to a question asked by A. R. Rivera and P. \v{S}parl in 2019 as well as the first example of tetravalent normal-edge-transitive non-normal Cayley graph on a nonabelian simple group.
Keywords
Cite
@article{arxiv.2512.21611,
title = {On automorphism groups of half-arc-transitive tetravalent graphs},
author = {Yuandong Li and Binzhou Xia and Jin-Xin Zhou},
journal= {arXiv preprint arXiv:2512.21611},
year = {2025}
}