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1.
Consistent Cycles in 1/2-Arc-Transitive Graphs
Marko Boben, Štefko Miklavič, Primož Potočnik, 2009, izvirni znanstveni članek

Najdeno v: osebi
Ključne besede: mathematics, graph theory, 1/2-arc-transitivity, consistent cycle
Objavljeno: 15.10.2013; Ogledov: 2095; Prenosov: 7
URL Polno besedilo (0,00 KB)
Gradivo ima več datotek! Več...

2.
Distance-regular Cayley graphs on dihedral groups
Štefko Miklavič, Primož Potočnik, 2007, izvirni znanstveni članek

Opis: The main result of this article is a classification of distance-regular Cayley graphs on dihedral groups. There exist four obvious families of such graphs, which are called trivial. These are: complete graphs, complete bipartite graphs, complete bipartite graphs with the edges of a 1-factor removed, and cycles. It is proved that every non-trivial distance-regular Cayley graph on a dihedral group is bipartite, non-antipodal, has diameter 3 and arises either from a cyclic di#erence set, or possibly (if any such exists) from a dihedral difference set satisfying some additional conditions. Finally, all distance-transitive Cayley graphs on dihedral groups are determined. It transpires that a Cayley graph on a dihedral group is distance-transitive if and only if it is trivial, or isomorphic to the incidence or to the non-incidence graph of a projective space ▫$\mathrm{PG}_{d-1} (d,q)$▫, ▫$d \ge 2$▫, or the unique pair of complementary symmetric designs on 11 vertices.
Najdeno v: osebi
Ključne besede: mathematics, grah theory, distance-regular graph, distance-transitive graph, Cayley graph, dihedral group, dihedrant, difference set
Objavljeno: 15.10.2013; Ogledov: 1203; Prenosov: 51
URL Polno besedilo (0,00 KB)

3.
Rotary polygons in configurations
Marko Boben, Štefko Miklavič, Primož Potočnik, 2011, izvirni znanstveni članek

Najdeno v: osebi
Ključne besede: konfiguracija, poligon, avtomorfizem, antiavtomorfizem
Objavljeno: 15.10.2013; Ogledov: 1378; Prenosov: 7
URL Polno besedilo (0,00 KB)
Gradivo ima več datotek! Več...

4.
Arc-transitive cycle decompositions of tetravalent graphs
Štefko Miklavič, Primož Potočnik, Stephen Wilson, 2008, izvirni znanstveni članek

Opis: A cycle decomposition of a graph ▫$\Gamma$▫ is a set ▫$\mathcal{C}$▫ of cycles of ▫$\Gamma$▫ such that every edge of ▫$\Gamma$▫ belongs to exactly one cycle in ▫$\mathcal{C}$▫. Such a decomposition is called arc-transitive if the group of automorphisms of ▫$\Gamma$▫ that preserve setwise acts transitively on the arcs of ▫$\Gamma$▫. In this paper, we study arc-transitive cycle decompositions of tetravalent graphs. In particular, we are interested in determining and enumerating arc-transitive cycle decompositions admitted by a given arc-transitive tetravalent graph. Among other results we show that a connected tetravalent arc-transitive graph is either 2-arc-transitive, or is isomorphic to the medial graph of a reflexible map, or admits exactly one cycle structure.
Najdeno v: osebi
Ključne besede: mathematics, graph theory, cycle decomposition, automorphism group, consistent cycle, medial maps
Objavljeno: 15.10.2013; Ogledov: 1340; Prenosov: 43
URL Polno besedilo (0,00 KB)

5.
Distance-regular Cayley graphs on dihedral groups
Primož Potočnik, Štefko Miklavič, 2005, izvirni znanstveni članek

Opis: The main result of this article is a classification of distance-regular Cayley graphs on dihedral groups. There exist four obvious families of such graphs, which are called trivial. These are: complete graphs, complete bipartite graphs, complete bipartite graphs with the edges of a 1-factor removed, and cycles. It is proved that every non-trivial distance-regular Cayley graph on a dihedral group is bipartite, non-antipodal, has diameter 3 and arises either from a cyclic di#erence set, or possibly (if any such exists) from a dihedral difference set satisfying some additional conditions. Finally, all distance-transitive Cayley graphs on dihedral groups are determined. It transpires that a Cayley graph on a dihedral group is distance-transitive if and only if it is trivial, or isomorphic to the incidence or to the non-incidence graph of a projective space ▫$\mathrm{PG}_{d-1} (d,q)$▫, ▫$d \ge 2$▫, or the unique pair of complementary symmetric designs on 11 vertices.
Najdeno v: osebi
Ključne besede: mathematics, grah theory, distance-regular graph, distance-transitive graph, Cayley graph, dihedral group, dihedrant, difference set
Objavljeno: 10.07.2015; Ogledov: 826; Prenosov: 39
URL Polno besedilo (0,00 KB)

6.
7.
Semisymmetric elementary abelian covers of the Möbius-Kantor graph
Aleksander Malnič, Štefko Miklavič, Primož Potočnik, Dragan Marušič, 2007, izvirni znanstveni članek

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.
Najdeno v: osebi
Ključne besede: mathematics, graph theory, graph, covering projection, lifting automorphisms, homology group, group representation, matrix group, invariant subspaces
Objavljeno: 03.04.2017; Ogledov: 736; Prenosov: 43
URL Polno besedilo (0,00 KB)

8.
Two-arc-transitive two-valent digraphs of certain orders
Katja Berčič, Primož Potočnik, 2016, izvirni znanstveni članek

Najdeno v: osebi
Ključne besede: graph, digraph, arc-transitive, order
Objavljeno: 08.08.2016; Ogledov: 879; Prenosov: 48
URL Polno besedilo (0,00 KB)

9.
Arc-transitive digraphs of given out-valency and with blocks of given size
Primož Potočnik, Luke Morgan, Gabriel Verret, 2019, izvirni znanstveni članek

Opis: Given integers ▫$k$▫ and ▫$m$▫, we construct a ▫$G$▫-arc-transitive graph of valency ▫$k$▫ and an ▫$L$▫-arc-transitive oriented digraph of out-valency ▫$k$▫ such that ▫$G$▫ and ▫$L$▫ both admit blocks of imprimitivity of size ▫$m$▫.
Najdeno v: osebi
Ključne besede: arc-transitive digraphs, Cayley digraphs, imprimitive digraphs
Objavljeno: 28.06.2019; Ogledov: 148; Prenosov: 70
URL Polno besedilo (0,00 KB)

10.
On reflexible polynomials
Aleksander Malnič, Boštjan Kuzman, Primož Potočnik, 2018, objavljeni povzetek znanstvenega prispevka na konferenci (vabljeno predavanje)

Najdeno v: osebi
Ključne besede: minimal elementary abelian cover, doubled cycle, polynomial
Objavljeno: 07.02.2018; Ogledov: 1091; Prenosov: 13
URL Polno besedilo (0,00 KB)

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