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201.
On the split structure of lifted groups
Aleksander 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: 2675; Prenosov: 157
.pdf Celotno besedilo (422,56 KB)

202.
203.
Half-arc-transitive group actions with a small number of alternets
Klavdija Kutnar, 2015, objavljeni povzetek znanstvenega prispevka na konferenci

Ključne besede: automorphism group, half-arc-tranistive graph, alternet
Objavljeno v RUP: 15.10.2015; Ogledov: 2313; Prenosov: 28
URL Povezava na celotno besedilo

204.
On the full automorphism group in vertex-transitive graphs
Dragan Marušič, 2015, objavljeni povzetek znanstvenega prispevka na konferenci

Ključne besede: odd automorphism, automorphism group, graph
Objavljeno v RUP: 15.10.2015; Ogledov: 2270; Prenosov: 35
URL Povezava na celotno besedilo

205.
Computational aspects of lifting automorphisms
Rok Požar, 2015, objavljeni povzetek znanstvenega prispevka na konferenci

Ključne besede: covering projection, graph, lifting automorphsim
Objavljeno v RUP: 15.10.2015; Ogledov: 2129; Prenosov: 13
URL Povezava na celotno besedilo

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209.
Some results on the index of unicyclic graphs
Francesco Belardo, Enzo M. Li Marzi, Slobodan Simić, 2006, izvirni znanstveni članek

Ključne besede: graph eigenvalues, graph index, unicyclic graphs
Objavljeno v RUP: 15.10.2015; Ogledov: 2323; Prenosov: 148
URL Povezava na celotno besedilo

210.
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