Vertex-primitive $s$-arc-transitive Cayley digraphs
Combinatorics
2026-05-05 v1 Group Theory
Abstract
Determining an upper bound on for vertex-primitive -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 , a complete classification for remains out of reach. In this paper, we prove that the tight upper bound on for finite vertex-primitive -arc-transitive Cayley digraphs is exactly . Furthermore, we completely characterize the structure of these digraphs when .
Cite
@article{arxiv.2605.01734,
title = {Vertex-primitive $s$-arc-transitive Cayley digraphs},
author = {Jing Jian Li and Yong Tang Shi and Yu Wang and Binzhou Xia},
journal= {arXiv preprint arXiv:2605.01734},
year = {2026}
}
Comments
14 pages