31. O ekstremnih grafih z dano stopnjo in premerom/ožino : doktorska disertacijaSlobodan Filipovski, 2018, doktorska disertacija Ključne besede: adjacency matrix, antipodal graphs, cages, excess, defect, Ramanujan graphs, selfrepeats, degree/diameter problem, spectrum, Moore graphs, asymptotic density, distance matrices, Bermond and Bollobas problem Objavljeno v RUP: 21.01.2019; Ogledov: 2744; Prenosov: 0 |
32. On the Terwilliger algebra of bipartite distance-regular graphs with $G_{i-1,i-1,1}(x, y, z) = alpha_i + beta_i G_{1,1,i%1}(x, y, z)$ : 31th Ljubljana - Leoben Graph Theory Seminar, September 3-4, 2018, LoebenSafet Penjić, 2018, prispevek na konferenci brez natisa Ključne besede: distance-regular graphs, Terwilliger algebra, irreducible modules Objavljeno v RUP: 17.09.2018; Ogledov: 1828; Prenosov: 26 Povezava na celotno besedilo |
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35. Characterizations of minimal dominating sets and the well-dominated property in lexicographic product graphsDidem Gozüpek, Ademir Hujdurović, Martin Milanič, 2017, izvirni znanstveni članek Ključne besede: lekisikografski product grafov, minimalna dominantna množica, dobro dominiran graf, nesvodljiva dominantna množica, lexicographic product of graphs, minimal dominating set, well-dominated graph, irreducible dominating set Objavljeno v RUP: 14.11.2017; Ogledov: 2209; Prenosov: 65 Povezava na celotno besedilo |
36. On the Terwilliger algebra of bipartite distance-regular graphs with [Delta][sub]2 = 0 and c[sub]2=1Mark 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. Ključne besede: distance-regular graphs, terwilliger algebra, subconstituent algebra Objavljeno v RUP: 14.11.2017; Ogledov: 2438; Prenosov: 143 Povezava na celotno besedilo |
37. Nove karakterizacije v strukturni teoriji grafov : 1-popolno usmerljivi grafi, produktni grafi in cena povezanostiTatiana Romina Hartinger, 2017, doktorska disertacija Ključne besede: 1-perfectly orientable graph, structural characterization of families of graphs, chordal graph, interval graph, circular arc graph, cograph, block-cactus graph, cobipartite graph, K4-minor-free graph, outerplanar graph, graph product, Cartesian product, lexicographic product, direct product, strong product, price of connectivity, cycle transversal, path transversal Objavljeno v RUP: 09.11.2017; Ogledov: 2697; Prenosov: 40 Povezava na celotno besedilo |
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39. On maximal distances in a commuting graphGregor Dolinar, Bojan Kuzma, Polona Oblak, 2012, izvirni znanstveni članek Opis: It is shown that matrices over algebraically closed fields that are farthest apart in the commuting graph must be non-derogatory. Rank-one matrices and diagonalizable matrices are also characterized in terms of the commuting graph. Ključne besede: matematika, linearna algebra, teorija grafov, komutirajoči grafi, matrična algebra, algebraično zaprt obseg, centralizator, razdalja v grafih, mathematics, linear algebra, graph theory, commuting graph, matrix algebra, algebraically closed field, centralizer, distance in graphs Objavljeno v RUP: 03.04.2017; Ogledov: 2390; Prenosov: 256 Povezava na celotno besedilo |
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