1. On bipartite Qpolynomial distanceregular graphs with c [sub] 2 [equal] 1Štefko Miklavič, 2007, original scientific article Abstract: Let ▫$\Gamma$▫ denote a bipartite ▫$Q$▫polynomial distanceregular graph with diameter ▫$d \ge 3$▫, valency ▫$k \ge 3$▫ and intersection number ▫$c_2=1$▫. We show that ▫$\Gamma$▫ has a certain equitable partition of its vertex set which involves ▫$4d4$▫ cells. We use this partition to show that the intersection numbers of ▫$\Gamma$▫ satisfy the following divisibility conditions: (I) ▫$c_{i+1}1$▫ divides ▫$c_i(c_i1)$▫ for ▫$2 \le i \le d1$▫, and (II) ▫$b_{i1}1$▫ divides ▫$b_i(b_i1)$▫ for ▫$1 \le i \le d1$▫. Using these divisibility conditions we show that ▫$\Gamma$▫ does not exist if ▫$d=4$▫. Found in: ključnih besedah Summary of found: ...mathematics, grah theory, distanceregular graphs, ▫$Q$▫polynomial property, equitable partitions... Keywords: mathematics, grah theory, distanceregular graphs, ▫$Q$▫polynomial property, equitable partitions Published: 15.10.2013; Views: 1777; Downloads: 15 Full text (0,00 KB) 
2. On bipartite Qpolynominal distanceregular graphsŠtefko Miklavič, 2007, original scientific article Abstract: Let ▫$\Gamma$▫ denote a bipartite ▫$Q$▫polynomial distanceregular graph with vertex set ▫$X$▫, diameter ▫$d \ge 3$▫ and valency ▫$k \ge 3$▫. Let ▫${\mathbb{R}}^X$▫ denote the vector space over ▫$\mathbb{R}$▫ consisting of column vectors with entries in ▫$\mathbb{r}$▫ and rows indexed by ▫$X$▫. For ▫$z \in X$▫, let ▫$\hat{z}$▫ denote the vector in ▫${\mathbb{R}}^X$▫ with a 1 in the ▫$z$▫coordinate, and 0 in all other coordinates. Fix ▫$x,y \in X$▫ such that ▫$\partial(x,y)=2▫, where ▫$\partial$▫ denotes the pathlength distance. For ▫$0 \le i,j \le d$▫ define ▫$w_{ij} = \sum\hat{z}$▫, where the sum is over all ▫$z \in X$▫ such that ▫$\partial(x,z) = i$▫ and ▫$\partial(y,z) = j▫$. We define ▫$W = \textrm{span} \{w_{ij}0 \le i,j \le d\}$▫. In this paper we consider the space ▫$MW = \textrm{span} \{mw m \in M, w \in W \l\}$▫, where ▫$M$▫ is the BoseMesner algebra of ▫$\Gamma$▫. We observe that ▫$MW$▫ is the minimal ▫$A$▫invariant subspace of ▫${\mathbb{R}}^X$▫ which contains ▫$W$▫, where ▫$A$▫ is the adjacency matrix of ▫$\Gamma$▫. We display a basis for ▫$MW$▫ that is orthogonal with respect to the dot product. We give the action of ▫$A$▫ on this basis. We show that the dimension of ▫$MW$▫ is ▫$3d3$▫ if ▫$\Gamma$▫ is 2homogeneous, ▫$3d1$▫ if ▫$\Gamma$▫ is the antipodal quotient of the ▫$2d$▫cube, and ▫$4d4$▫ otherwise. We obtain our main result using Terwilliger's "balanced set" characterization of the ▫$Q$▫polynomial property. Found in: ključnih besedah Summary of found: ...Terwilliger's "balanced set" characterization of the ▫$Q$▫polynomial property.... Keywords: mathematics, graph theory, distanceregular graphs, ▫$Q$▫polynominal property, BoseMesner algebra, balanced set characterization of the Qpolynominal property Published: 15.10.2013; Views: 1596; Downloads: 12 Full text (0,00 KB) 
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4. Ownership restructuring in transition societies from historic perspectiveAndrej Bertoncelj, Matjaž Nahtigal, 2013, original scientific article Found in: ključnih besedah Summary of found: ...private property, mass privatization, historical background, regulatory legal framework,... Keywords: private property, mass privatization, historical background, regulatory legal framework, transition societies, Arab spring, Mediterranean countries Published: 21.12.2015; Views: 1259; Downloads: 11 Full text (0,00 KB) 
5. Historical transformation of property rights in the context of new paradigm of human developmentRado Bohinc, 2013, original scientific article Found in: ključnih besedah Summary of found: Zadetek v naslovu Keywords: property rights, definition of property, historical transformation, property, contemporary economic paradigm, profit sharing, social responsibility, social enterpreneurship Published: 21.12.2015; Views: 1185; Downloads: 13 Full text (0,00 KB) 
6. Reachability relations in digraphsNorbert Seifter, Boris Zgrablić, Aleksander Malnič, Primož Šparl, Dragan Marušič, 2008, original scientific article Abstract: In this paper we study reachability relations on vertices of digraphs, informally defined as follows. First, the weight of a walk is equal to the number of edges traversed in the direction coinciding with their orientation, minus the number of edges traversed in the direction opposite to their orientation. Then, a vertex ▫$u$▫ is ▫$R_k^+$▫related to a vertex ▫$v$▫ if there exists a 0weighted walk from ▫$u$▫ to ▫$v$▫ whose every subwalk starting at u has weight in the interval ▫$[0,k]$▫. Similarly, a vertex ▫$u$▫ is ▫$R_k^$▫related to a vertex ▫$v$▫ if there exists a 0weighted walk from ▫$u$▫ to ▫$v$▫ whose every subwalk starting at ▫$u$▫ has weight in the interval ▫$[k,0]$▫. For all positive integers ▫$k$▫, the relations ▫$R_k^+$▫ and ▫$R_k^$▫ are equivalence relations on the vertex set of a given digraph. We prove that, for transitive digraphs, properties of these relations are closely related to other properties such as having property ▫$\mathbb{Z}$▫, the number of ends, growth conditions, and vertex degree. Found in: ključnih besedah Summary of found: ...related to other properties such as having property ▫$\mathbb{Z}$▫, the number of ends, growth conditions,... Keywords: graph theory, digraph, reachability relations, end of a graph, property ▫$\mathbb{Z}$▫, growth Published: 03.04.2017; Views: 893; Downloads: 83 Full text (0,00 KB) 
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8. Cyclic groups are CIgroups for balanced configurationsMikhail Muzychuk, Dragan Marušič, István Kovács, Sergio Hiroki Koike Quintanar, 2018, original scientific article Found in: ključnih besedah Summary of found: ...Cayley object, CIproperty, cyclic group, balanced configuration... Keywords: Cayley object, CIproperty, cyclic group, balanced configuration Published: 20.07.2018; Views: 1006; Downloads: 167 Full text (0,00 KB) This document has more files! More...

9. O Terwilligerjevi algebri dvodelnih razdaljnoregularnih grafovSafet Penjić, 2019, doctoral dissertation Found in: ključnih besedah Summary of found: ...stanceregular graph, Terwilliger algebra, subconstituent algebra, Qpolynomial property, equitable partition... Keywords: bipartite distanceregular graph, Terwilliger algebra, subconstituent algebra, Qpolynomial property, equitable partition Published: 04.06.2019; Views: 389; Downloads: 9 Full text (0,00 KB) 
10. On the König deficiency of zeroreducible graphsMiklós Bartha, Miklós Ferenz Krész, 2019, original scientific article Found in: ključnih besedah Summary of found: ...graph matching, independent set, König property, graph reduction, graph algorithm... Keywords: graph matching, independent set, König property, graph reduction, graph algorithm Published: 14.11.2019; Views: 107; Downloads: 13 Full text (0,00 KB) 