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61.
Cayley graphs on abelian groups
Edward Dobson, Pablo Spiga, Gabriel Verret, 2015, original scientific article

Keywords: Cayley graph, abelian group, automorphism
Published in RUP: 03.04.2017; Views: 2262; Downloads: 136
URL Link to full text

62.
Quotients of CI-Groups are CI-Groups
Edward Dobson, Joy Morris, 2015, original scientific article

Keywords: CI-group, Cayley graph, Quotient
Published in RUP: 03.04.2017; Views: 2065; Downloads: 139
URL Link to full text

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65.
Lower bounds on the simultaneous conjugacy problem in the symmetric group
Rok Požar, Andrej Brodnik, Aleksander Malnič, 2015, published scientific conference contribution abstract

Keywords: communication complexity, lower bound, symmetric group
Published in RUP: 08.08.2016; Views: 2421; Downloads: 42
URL Link to full text

66.
On colour-preserving automorphisms of Cayley graphs
Klavdija Kutnar, Ademir Hujdurović, Edward Dobson, Dave Witte Morris, Joy Morris, 2016, published scientific conference contribution abstract

Keywords: Cayley graph, automorphism, group, colouring
Published in RUP: 08.08.2016; Views: 2566; Downloads: 87
URL Link to full text

67.
Symmetry of graphs via even/odd automorphisms
Dragan Marušič, Klavdija Kutnar, 2016, published scientific conference contribution abstract (invited lecture)

Keywords: vertex-transitive, graph, odd automorphism, automorphism group
Published in RUP: 08.08.2016; Views: 2085; Downloads: 26
URL Link to full text

68.
On the split structure of lifted groups
Aleksander Malnič, Rok Požar, 2016, original scientific article

Abstract: 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.
Keywords: algorithm, abelian cover, Cayley voltages, covering projection, graph, group extension, group presentation, lifting automorphisms, linear systems over the integers, semidirect product
Published in RUP: 15.10.2015; Views: 2673; Downloads: 157
.pdf Full text (422,56 KB)

69.
Half-arc-transitive group actions with a small number of alternets
Klavdija Kutnar, 2015, published scientific conference contribution abstract

Keywords: automorphism group, half-arc-tranistive graph, alternet
Published in RUP: 15.10.2015; Views: 2312; Downloads: 28
URL Link to full text

70.
On the full automorphism group in vertex-transitive graphs
Dragan Marušič, 2015, published scientific conference contribution abstract

Keywords: odd automorphism, automorphism group, graph
Published in RUP: 15.10.2015; Views: 2250; Downloads: 35
URL Link to full text

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