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31.
Editorial
Štefko Miklavič, Primož Šparl, Klavdija Kutnar, Tomaž Pisanski, 2015, predgovor, spremna beseda

Najdeno v: osebi
Objavljeno: 15.10.2015; Ogledov: 778; Prenosov: 9
URL Polno besedilo (0,00 KB)

32.
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: 836; Prenosov: 53
URL Polno besedilo (0,00 KB)

33.
Kode za popravljanje napak
Aljaž Slivnik, 2010, magistrsko delo

Najdeno v: osebi
Ključne besede: končni obseg, vektorski prostor, linearna koda, generatorska matrika, kontrolna matrika, ciklična koda, Reed-Solomonova koda
Objavljeno: 13.11.2017; Ogledov: 541; Prenosov: 14
URL Polno besedilo (0,00 KB)
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34.
Hamiltonskost cayleyevih (di)grafov abelskih grup
Alenka Močnik, 2009, magistrsko delo

Najdeno v: osebi
Ključne besede: grupa, abelska grupa, (di)graf, hamiltonov cikel, cayleyev (di)graf, Lovászevo vprašanje
Objavljeno: 13.11.2017; Ogledov: 521; Prenosov: 12
URL Polno besedilo (0,00 KB)

35.
On the Terwilliger algebra of bipartite distance-regular graphs with [Delta][sub]2 = 0 and c[sub]2=1
Mark MacLean, Štefko Miklavič, Safet Penjić, 2016, izvirni znanstveni članek

Opis: Let ▫$\Gamma$▫ denote a bipartite distance-regular graph with diameter ▫$D \geq 4$▫ and valency ▫$k \geq 3$▫. Let ▫$X$▫ denote the vertex set of ▫$\Gamma$▫, and let ▫$A$▫ denote the adjacency matrix of ▫$\Gamma$▫. For ▫$x \in X$▫ and for ▫$0 \leq i \leq D$▫, let ▫$\operatorname{\Gamma}_i(x)$▫ denote the set of vertices in ▫$X$▫ that are distance ▫$i$▫ from vertex ▫$x$▫. Define a parameter ▫$\operatorname{\Delta}_2$▫ in terms of the intersection numbers by ▫$\operatorname{\Delta}_2 = (k - 2)(c_3 - 1) -(c_2 - 1) p_{22}^2$▫. We first show that ▫$\operatorname{\Delta}_2 = 0$▫ implies that ▫$D \leq 5$▫ or ▫$c_2 \in \{1, 2 \}$▫. For ▫$x \in X$▫ let ▫$T = T(x)$▫ denote the subalgebra of ▫$\text{Mat}_X(\mathbb{C})$▫ generated by ▫$A, E_0^\ast, E_1^\ast, \ldots, E_D^\ast$▫, where for ▫$0 \leq i \leq D$, $E_i^\ast$▫ represents the projection onto the▫ $i$▫th subconstituent of ▫$\Gamma$▫ with respect to ▫$x$▫. We refer to ▫$T$▫ as the Terwilliger algebra of ▫$\Gamma$▫ with respect to ▫$x$▫. By the endpoint of an irreducible ▫$T$▫-module ▫$W$▫ we mean ▫$\min \{i | E_i^\ast W \ne 0 \}$▫. In this paper we assume ▫$\Gamma$▫ has the property that for ▫$2 \leq i \leq D - 1$▫, there exist complex scalars ▫$\alpha_i$▫, ▫$\beta_i$▫ such that for all ▫$x, y, z \in X$▫ with ▫$\partial(x, y) = 2$▫, ▫$\partial(x, z) = i$▫, ▫$\partial(y, z) = i$▫, we have ▫$\alpha_i + \beta_i | \operatorname{\Gamma}_1(x) \cap \operatorname{\Gamma}_1(y) \cap \operatorname{\Gamma}_{i - 1}(z) | = | \operatorname{\Gamma}_{i - 1}(x) \cap \operatorname{\Gamma}_{i - 1}(y) \cap \operatorname{\Gamma}_1(z) |$▫. We additionally assume that▫ $\operatorname{\Delta}_2 = 0$▫ with ▫$c_2 = 1$▫. Under the above assumptions we study the algebra ▫$T$▫. We show that if ▫$\Gamma$▫ is not almost 2-homogeneous, then up to isomorphism there exists exactly one irreducible ▫$T$▫-module with endpoint 2. We give an orthogonal basis for this ▫$T$▫-module, and we give the action of ▫$A$▫ on this basis.
Najdeno v: osebi
Ključne besede: distance-regular graphs, terwilliger algebra, subconstituent algebra
Objavljeno: 14.11.2017; Ogledov: 632; Prenosov: 47
URL Polno besedilo (0,00 KB)

36.
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On 2-distance-balanced graphs
Boštjan Frelih, Štefko Miklavič, 2018, izvirni znanstveni članek

Najdeno v: osebi
Ključne besede: n-distance-balanced graph, cartesian product, lexicographic product
Objavljeno: 07.02.2018; Ogledov: 1297; Prenosov: 67
URL Polno besedilo (0,00 KB)

39.
40.
On bipartite Q-polynomial distance-regular graphs with diameter 9, 10, or 11
Štefko Miklavič, 2018, izvirni znanstveni članek

Najdeno v: osebi
Ključne besede: bipartite distance-regular graph, Q-polynomial property, isomorphism
Objavljeno: 12.03.2018; Ogledov: 1256; Prenosov: 26
URL Polno besedilo (0,00 KB)

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