Vertex-primitive $s$-arc-transitive Cayley digraphs
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866913084326543360 |
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| author | Li, Jing Jian Shi, Yong Tang Wang, Yu Xia, Binzhou |
| author_facet | Li, Jing Jian Shi, Yong Tang Wang, Yu Xia, Binzhou |
| contents | Determining an upper bound on $s$ for vertex-primitive $s$-arc-transitive digraphs has been an open problem of considerable interest since a question asked by Praeger in 1990. Although much progress has been made and an upper bound is conjectured to be $2$, a complete classification for $s=2$ remains out of reach. In this paper, we prove that the tight upper bound on $s$ for finite vertex-primitive $s$-arc-transitive Cayley digraphs is exactly $2$. Furthermore, we completely characterize the structure of these digraphs when $s=2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_01734 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Vertex-primitive $s$-arc-transitive Cayley digraphs Li, Jing Jian Shi, Yong Tang Wang, Yu Xia, Binzhou Combinatorics Group Theory 05C20, 05C25 Determining an upper bound on $s$ for vertex-primitive $s$-arc-transitive digraphs has been an open problem of considerable interest since a question asked by Praeger in 1990. Although much progress has been made and an upper bound is conjectured to be $2$, a complete classification for $s=2$ remains out of reach. In this paper, we prove that the tight upper bound on $s$ for finite vertex-primitive $s$-arc-transitive Cayley digraphs is exactly $2$. Furthermore, we completely characterize the structure of these digraphs when $s=2$. |
| title | Vertex-primitive $s$-arc-transitive Cayley digraphs |
| topic | Combinatorics Group Theory 05C20, 05C25 |
| url | https://arxiv.org/abs/2605.01734 |