English

On automorphism groups of half-arc-transitive tetravalent graphs

Group Theory 2025-12-29 v1 Combinatorics

Abstract

We characterize connected tetravalent graphs Γ\Gamma which admit groups M<HM<H of automorphisms such that Γ\Gamma is MM-half-arc-transitive and HH-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}
}