English

Bounding $s$ for vertex-primitive $s$-arc-transitive digraphs of alternating and symmetric groups

Combinatorics 2024-02-23 v2

Abstract

Determining an upper bound on ss for finite vertex-primitive ss-arc-transitive digraphs has received considerable attention dating back to a question of Praeger in 1990. It was shown by Giudici and Xia that the smallest upper bound on ss is attained for some digraph admitting an almost simple ss-arc-transitive group. In this paper, based on the work of Pan, Wu and Yin, we prove that s2s\leqslant 2 in the case where the group is an alternating or symmetric group.

Keywords

Cite

@article{arxiv.2111.06579,
  title  = {Bounding $s$ for vertex-primitive $s$-arc-transitive digraphs of alternating and symmetric groups},
  author = {Junyan Chen and Lei Chen and Michael Giudici and Jing Jian Li and Cheryl E. Praeger and Binzhou Xia},
  journal= {arXiv preprint arXiv:2111.06579},
  year   = {2024}
}