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Title:Semisymmetric elementary abelian covers of the Möbius-Kantor graph
Authors:ID Malnič, Aleksander (Author)
ID Marušič, Dragan (Author)
ID Miklavič, Štefko (Author)
ID Potočnik, Primož (Author)
Files:URL http://dx.doi.org/10.1016/j.disc.2006.10.008
 
Language:English
Work type:Not categorized
Typology:1.01 - Original Scientific Article
Organization:IAM - Andrej Marušič Institute
Abstract:Let N:˜XX 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 N is called p-elementary abelian. The projection N is vertex-transitive (edge-transitive) if some vertex-transitive (edge-transitive) subgroup of Aut X lifts along N, and semisymmetric if it is edge- but not vertex-transitive. The projection N is minimal semisymmetric if N cannot be written as a composition N=M of two (nontrivial) regular covering projections, where \pwM 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 (p1)/4 and 1+(p1)/4 in cases p5,9,13,17,21(mod24) and p1(mod24), respectively, and to (p+1)/4 and 1+(p+1)/4 in cases p3,7,11,15,23(mod24) and p19(mod24), respectively. For each such covering projection the voltage rules generating the corresponding covers are displayed explicitly.
Keywords:mathematics, graph theory, graph, covering projection, lifting automorphisms, homology group, group representation, matrix group, invariant subspaces
Year of publishing:2007
Number of pages:str. 2156-2175
Numbering:Vol. 307, iss. 17-18
PID:20.500.12556/RUP-7723 This link opens in a new window
ISSN:0012-365X
UDC:519.17
COBISS.SI-ID:14337113 This link opens in a new window
Publication date in RUP:03.04.2017
Views:3003
Downloads:92
Metadata:XML DC-XML DC-RDF
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MALNIČ, Aleksander, MARUŠIČ, Dragan, MIKLAVIČ, Štefko and POTOČNIK, Primož, 2007, Semisymmetric elementary abelian covers of the Möbius-Kantor graph. [online]. 2007. Vol. 307, no. 17–18, p. 2156–2175. [Accessed 4 April 2025]. Retrieved from: http://dx.doi.org/10.1016/j.disc.2006.10.008
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Secondary language

Language:English
Keywords:matematika, teorija grafov, graf, krovna projekcija, dvig avtomorfizmov, homološka grupa, matrična grupa, invariantni podprostori


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