| Naslov: | Semisymmetric elementary abelian covers of the Möbius-Kantor graph |
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| Avtorji: | ID Malnič, Aleksander (Avtor)
ID Marušič, Dragan (Avtor)
ID Miklavič, Štefko (Avtor)
ID Potočnik, Primož (Avtor) |
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| Datoteke: |  http://dx.doi.org/10.1016/j.disc.2006.10.008
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| Jezik: | Angleški jezik |
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| Vrsta gradiva: | Delo ni kategorizirano |
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| Tipologija: | 1.01 - Izvirni znanstveni članek |
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| Organizacija: | IAM - Inštitut Andrej Marušič
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| Opis: | 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. |
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| Ključne besede: | mathematics, graph theory, graph, covering projection, lifting automorphisms, homology group, group representation, matrix group, invariant subspaces |
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| Leto izida: | 2007 |
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| Št. strani: | str. 2156-2175 |
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| Številčenje: | Vol. 307, iss. 17-18 |
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| PID: | 20.500.12556/RUP-7723  |
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| ISSN: | 0012-365X |
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| UDK: | 519.17 |
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| COBISS.SI-ID: | 14337113 |
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| Datum objave v RUP: | 02.04.2017 |
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| Število ogledov: | 2739 |
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| Število prenosov: | 89 |
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| Metapodatki: |    |
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