On automorphism groups of half-arc-transitive tetravalent graphs
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909975913168896 |
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| author | Li, Yuandong Xia, Binzhou Zhou, Jin-Xin |
| author_facet | Li, Yuandong Xia, Binzhou Zhou, Jin-Xin |
| contents | We characterize connected tetravalent graphs $Γ$ which admit groups $M<H$ of automorphisms such that $Γ$ 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. Šparl in 2019 as well as the first example of tetravalent normal-edge-transitive non-normal Cayley graph on a nonabelian simple group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_21611 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On automorphism groups of half-arc-transitive tetravalent graphs Li, Yuandong Xia, Binzhou Zhou, Jin-Xin Group Theory Combinatorics We characterize connected tetravalent graphs $Γ$ which admit groups $M<H$ of automorphisms such that $Γ$ 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. Šparl in 2019 as well as the first example of tetravalent normal-edge-transitive non-normal Cayley graph on a nonabelian simple group. |
| title | On automorphism groups of half-arc-transitive tetravalent graphs |
| topic | Group Theory Combinatorics |
| url | https://arxiv.org/abs/2512.21611 |