1. 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: 322; Prenosov: 1
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8. On the split structure of lifted groupsAleksander Malnič, Rok Požar, 2016, izvirni znanstveni članek Opis: Let ▫$\wp \colon \tilde{X} \to X$▫ be a regular covering projection of connected graphs with the group of covering transformations ▫$\rm{CT}_\wp$▫ being abelian. Assuming that a group of automorphisms ▫$G \le \rm{Aut} X$▫ lifts along $\wp$ to a group ▫$\tilde{G} \le \rm{Aut} \tilde{X}$▫, the problem whether the corresponding exact sequence ▫$\rm{id} \to \rm{CT}_\wp \to \tilde{G} \to G \to \rm{id}$▫ splits is analyzed in detail in terms of a Cayley voltage assignment that reconstructs the projection up to equivalence. In the above combinatorial setting the extension is given only implicitly: neither ▫$\tilde{G}$▫ nor the action ▫$G\to \rm{Aut} \rm{CT}_\wp$▫ nor a 2-cocycle ▫$G \times G \to \rm{CT}_\wp$▫, are given. Explicitly constructing the cover ▫$\tilde{X}$▫ together with ▫$\rm{CT}_\wp$▫ and ▫$\tilde{G}$▫ as permutation groups on ▫$\tilde{X}$▫ is time and space consuming whenever ▫$\rm{CT}_\wp$▫ is large; thus, using the implemented algorithms (for instance, HasComplement in Magma) is far from optimal. Instead, we show that the minimal required information about the action and the 2-cocycle can be effectively decoded directly from voltages (without explicitly constructing the cover and the lifted group); one could then use the standard method by reducing the problem to solving a linear system of equations over the integers. However, along these lines we here take a slightly different approach which even does not require any knowledge of cohomology. Time and space complexity are formally analyzed whenever ▫$\rm{CT}_\wp$▫ is elementary abelian.
Ključne besede: algorithm, abelian cover, Cayley voltages, covering projection, graph, group extension, group presentation, lifting automorphisms, linear systems over the integers, semidirect product
Objavljeno v RUP: 15.10.2015; Ogledov: 4379; Prenosov: 170
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9. Algebraični aspekti teorije grafov : doktorska disertacijaAdemir Hujdurović, 2013, doktorska disertacija Ključne besede: circulant, bicirculant, semiregular automorphism, vertex-transitive graph, half-arc-transitive graph, snark, Cayley graph, quasi m-Cayley graph, generalized Cayley graph, I-regular action, regular cover of a graph, automorphism group
Objavljeno v RUP: 10.07.2015; Ogledov: 5983; Prenosov: 53
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