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arXiv · 2512.21611

On automorphism groups of half-arc-transitive tetravalent graphs

Yuandong Li·Binzhou Xia·Jin-Xin Zhou
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Abstract

We characterize connected tetravalent graphs $\Gamma$ which admit groups $M<H$ of automorphisms such that $\Gamma$ is $M$-half-arc-transitive and $H$-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.

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Yuandong Li, Binzhou Xia, Jin-Xin Zhou. 2025-12-25. On automorphism groups of half-arc-transitive tetravalent graphs. https://arxiv.org/abs/2512.21611

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