1. Normality of quartic cayley graphs on regular ▫$p$▫-groups : a CFSG-free approachKlavdija Kutnar, Aleksander Malnič, Dragan Marušič, 2026, izvirni znanstveni članek Opis: Relying on the Classification of Finite Simple Groups it was shown by Feng and Xu (Discrete Math., 2005) that every quartic Cayley graph of a regular $p$-group, $p \neq 2,5$, is normal. In this paper a CFSG-free proof of a special case of Feng-Xu theorem is given. Along the way it is also proved that for an arbitrary $p$-group $G$ with a minimum set $\{a,b\}$ of two generators, one of which is of order $p$, in the corresponding Cayley graph $\mathrm{Cay}(G,\{a,a^{-1},b,b^{-1}\})$ the induced action of vertex stabilizer on the neighbors' set is contained in the dihedral group $D_8$.
Ključne besede: classification of finite simple groups, regular p-group, p-groups of exponent p, Cayley graph, normal graph, automorphism group
Objavljeno v RUP: 23.09.2026; Ogledov: 289; Prenosov: 5
 Celotno besedilo (612,50 KB)
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2. Basic tetravalent oriented graphs of independent-cycle typeNemanja 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: 1048; Prenosov: 9
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