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arXiv · 2605.01734

Vertex-primitive $s$-arc-transitive Cayley digraphs

Jing Jian Li·Yong Tang Shi·Yu Wang·Binzhou Xia
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Abstract

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 $s=2$.

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Jing Jian Li, Yong Tang Shi, Yu Wang, Binzhou Xia. 2026-05-03. Vertex-primitive $s$-arc-transitive Cayley digraphs. https://arxiv.org/abs/2605.01734

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