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1.
Covering space techniques in graph theory
Aleksander Malnič, 2010, published scientific conference contribution abstract

Found in: ključnih besedah
Summary of found: ...graph theory, graph covers, lifting automorphisms, ...
Keywords: graph theory, graph covers, lifting automorphisms
Published: 15.10.2013; Views: 1958; Downloads: 29
URL Full text (0,00 KB)
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2.
On the split structure of lifted groups
Aleksander Malnič, Rok Požar, 2016, original scientific article

Found in: ključnih besedah
Summary of found: ...covering projection, graph, group extension, group presentation, lifting automorphisms, linear systems over the integers, semidirect...
Keywords: algorithm, abelian cover, Cayley voltages, covering projection, graph, group extension, group presentation, lifting automorphisms, linear systems over the integers, semidirect product
Published: 15.10.2015; Views: 1047; Downloads: 61
URL Full text (0,00 KB)

3.
Semisymmetric elementary abelian covers of the Möbius-Kantor graph
Aleksander Malnič, Štefko Miklavič, Primož Potočnik, Dragan Marušič, 2007, original scientific article

Abstract: Let ▫$\wp_N : \tilde{X} \to X$▫ be a regular covering projection of connected graphs with the group of covering transformations isomorphic to ▫$N$▫. If ▫$N$▫ is an elementary abelian ▫$p$▫-group, then the projection ▫$\wp_N$▫ is called ▫$p$▫-elementary abelian. The projection ▫$\wp_N$▫ is vertex-transitive (edge-transitive) if some vertex-transitive (edge-transitive) subgroup of Aut ▫$X$▫ lifts along ▫$\wp_N$▫, and semisymmetric if it is edge- but not vertex-transitive. The projection ▫$\wp_N$▫ is minimal semisymmetric if ▫$\wp_N$▫ cannot be written as a composition ▫$\wp_N = \wp \circ \wp_M$▫ of two (nontrivial) regular covering projections, where ▫$\pw_M$▫ is semisymmetric. Finding elementary abelian covering projections can be grasped combinatorially via a linear representation of automorphisms acting on the first homology group of the graph. The method essentially reduces to finding invariant subspaces of matrix groups over prime fields (see [A. Malnic, D. Marušic, P. Potocnik, Elementary abelian covers of graphs, J. Algebraic Combin. 20 (2004) 71-97]). In this paper, all pairwise nonisomorphic minimal semisymmetric elementary abelian regular covering projections of the Möbius-Kantor graph, the Generalized Petersen graph GP(8,3), are constructed. No such covers exist for ▫$p=2$▫. Otherwise, the number of such covering projections is equal to ▫$(p-1)/4$▫ and ▫$1+(p-1)/4$▫ in cases ▫$p \equiv 5,9,13,17,21 \pmod{24}$▫ and ▫$p \equiv 1 \pmod{24}$▫, respectively, and to ▫$(p+1)/4$▫ and ▫$1+(p+1)/4$▫ in cases ▫$p \equiv 3,7,11,15,23 \pmod{24}$▫ and ▫$p \equiv 19 \pmod{24}$▫, respectively. For each such covering projection the voltage rules generating the corresponding covers are displayed explicitly.
Found in: ključnih besedah
Summary of found: ...mathematics, graph theory, graph, covering projection, lifting automorphisms, homology group, group representation, matrix group,...
Keywords: mathematics, graph theory, graph, covering projection, lifting automorphisms, homology group, group representation, matrix group, invariant subspaces
Published: 03.04.2017; Views: 812; Downloads: 51
URL Full text (0,00 KB)

4.
On split liftings with sectional complements
Aleksander Malnič, Rok Požar, 2018, original scientific article

Found in: ključnih besedah
Summary of found: ...covering projection, graph, group presentation, invariant section, lifting automorphisms, linear systems over the integers, split...
Keywords: algorithm, Cayley voltages, covering projection, graph, group presentation, invariant section, lifting automorphisms, linear systems over the integers, split extension
Published: 02.03.2018; Views: 587; Downloads: 96
URL Full text (0,00 KB)

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