31. |
32. Semisymmetric elementary abelian covers of the Möbius-Kantor graphAleksander Malnič, Dragan Marušič, Štefko Miklavič, Primož Potočnik, 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. Ključne besede: mathematics, graph theory, graph, covering projection, lifting automorphisms, homology group, group representation, matrix group, invariant subspaces Objavljeno v RUP: 03.04.2017; Ogledov: 2408; Prenosov: 86 Povezava na celotno besedilo |
33. |
34. |
35. Bounding the order of the vertex-stabiliser in 3-valent vertex-transitive and 4-valent arc-transitive graphsPrimož Potočnik, Pablo Spiga, Gabriel Verret, 2015, izvirni znanstveni članek Ključne besede: valenca 3, valenca 4, točkovna tranzitivnost, ločna tranzitivnost, lokalno-diedrski, valency 3, valency 4, vertex-transitive, arc-transitive, locally-dihedral Objavljeno v RUP: 15.10.2015; Ogledov: 3007; Prenosov: 201 Povezava na celotno besedilo |
36. Peer coaching for effective workplace learningBlanka Tacer, Kristina Potočnik, 2015, objavljeni povzetek znanstvenega prispevka na konferenci Ključne besede: učenje, delo, kompetence, usposobljenost, povzetki, professional growth, learning, coaching, abstracts Objavljeno v RUP: 14.10.2015; Ogledov: 2903; Prenosov: 78 Povezava na celotno besedilo |
37. |
38. |
39. |
40. Distance-regular Cayley graphs on dihedral groupsŠtefko Miklavič, Primož Potočnik, 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. Ključne besede: mathematics, grah theory, distance-regular graph, distance-transitive graph, Cayley graph, dihedral group, dihedrant, difference set Objavljeno v RUP: 10.07.2015; Ogledov: 2548; Prenosov: 90 Povezava na celotno besedilo |