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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, izvirni znanstveni članek

Opis: 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.
Ključne besede: digraph, vertex-primitive, s-arc-transitive, alternating group, symmetric group
Objavljeno v RUP: 22.10.2025; Ogledov: 385; Prenosov: 3
Celotno besedilo (397,42 KB)

Basic tetravalent oriented graphs of independent-cycle type
Nemanja Poznanović, Cheryl E. Praeger, 2025, izvirni znanstveni članek

Opis: 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).
Ključne besede: half-arc-transitive, vertex-transitive graph, edge-transitive graph, normal cover, cycle graph
Objavljeno v RUP: 21.10.2025; Ogledov: 456; Prenosov: 2
Celotno besedilo (398,19 KB)

Bounds for finite semiprimitive permutation groups : order, base size, and minimal degree
Luke Morgan, Cheryl E. Praeger, Kyle Rosa, 2020, izvirni znanstveni članek

Ključne besede: permutation groups, base size, minimal degree
Objavljeno v RUP: 02.12.2020; Ogledov: 2604; Prenosov: 39
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