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Bounding s for vertex-primitive s-arc-transitive digraphs of alternating and symmetric groups
Junyan Chen, Lei Chen, Michael Giudici, Jing Jian Li, Cheryl E. Praeger, Binzhou Xia, 2025, original scientific article

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<=2 in the case where the group is an alternating or symmetric group.
Keywords: digraph, vertex-primitive, s-arc-transitive, alternating group, symmetric group
Published in RUP: 22.10.2025; Views: 316; Downloads: 1
Full text (397,42 KB)

Basic tetravalent oriented graphs of independent-cycle type
Nemanja Poznanović, Cheryl E. Praeger, 2025, original scientific article

Abstract: The family OG(4) consisting of graph-group pairs (Γ, G), where Γ is a finite, connected, 4-valent graph admitting a G-vertex-, and G-edge-transitive, but not G-arc-transitive action, has recently been examined using a normal quotient methodology. A subfamily of OG(4) has been identified as ‘basic’, due to the fact that all members of OG(4) are normal covers of at least one basic pair. We provide an explicit classification of those basic pairs (Γ, G) which have at least two independent cyclic G-normal quotients (these are G-normal quotients which are not extendable to a common cyclic normal quotient).
Keywords: half-arc-transitive, vertex-transitive graph, edge-transitive graph, normal cover, cycle graph
Published in RUP: 21.10.2025; Views: 382; Downloads: 1
Full text (398,19 KB)

Bounds for finite semiprimitive permutation groups : order, base size, and minimal degree
Luke Morgan, Cheryl E. Praeger, Kyle Rosa, 2020, original scientific article

Keywords: permutation groups, base size, minimal degree
Published in RUP: 02.12.2020; Views: 2506; Downloads: 39
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