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

2021/11/12 by Chen, Junyan, Chen, Lei, Giudici, Michael +3
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2111.06579

Abstract

Determining an upper bound on s for finite vertex-primitive s-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 s is attained for some digraph admitting an almost simple s-arc-transitive group. In this paper, based on the work of Pan, Wu and Yin, we prove that s\leqslant 2 in the case where the group is an alternating or symmetric group.

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