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... Keywords: mathematics, grah theory, distanceregular graphs, ▫$Q$▫polynomial property, equitable partitions Published: 15.10.2013; Views: 3262; Downloads: 35 Full text (0,00 KB) 
2. Isomorphism checking of IgraphsTomaž Pisanski, Boris Horvat, Arjana Žitnik, 2012, original scientific article Abstract: We consider the class of ▫$I$▫graphs, which is a generalization of the class of the generalized Petersen graphs. We show that two ▫$I$▫graphs ▫$I(n, j, k)$▫ and ▫$I(n, j_1, k_1)$▫ are isomorphic if and only if there exists an integer ▫$a$▫ relatively prime to $n$ such that either ▫$\{j_1, k_1\} = \{aj \mod n, \; ak \mod n \}$▫ or ▫$\{j_1, k_1\} = \{aj \mod n, \; ak \mod n\}$▫. This result has an application in the enumeration of nonisomorphic ▫$I$▫graphs and unitdistance representations of generalized Petersen graphs. Found in: ključnih besedah Summary of found: ...mathematics, graph theory, isomorphism, Igraph, generalized Petersen graph... Keywords: mathematics, graph theory, isomorphism, Igraph, generalized Petersen graph Published: 15.10.2013; Views: 3116; Downloads: 130 Full text (0,00 KB) 
3. Rankpermutable additive mappingsAleksandr Èmilevič Guterman, Anna A. Alieva, Bojan Kuzma, 2006, original scientific article Abstract: Let ▫$\sigma$▫ be a fixed nonidentical permutation on ▫$k$▫ elements. Additive bijections ▫$T$▫ on the matrix algebra ▫$M_n(\mathbb{F})$▫ over a field ▫$\mathbb{F}$▫ of characteristic zero, with the property that ▫$\rm{rk} (A_1...A_k) = \rm{rk} (A_{\sigma(1)}...A_{\sigma(k)})$▫ implies the same condition on the ▫$T$▫ images, are characterized. It is also shown that the surjectivity assumption can be relaxed, if this property is preserved in both directions. Found in: ključnih besedah Summary of found: ...mathematics, linearna algebra, matrix algebra, rank, permutation, additive... Keywords: mathematics, linearna algebra, matrix algebra, rank, permutation, additive preservers Published: 15.10.2013; Views: 2631; Downloads: 85 Full text (0,00 KB) 
4. Identities with generalized skew derivations on Lie idealsAjda Fošner, Vincenzo De Filippis, Feng Wei, 2013, original scientific article Abstract: Let ▫$m, n$▫ be two nonzero fixed positive integers, ▫$R$▫ a 2torsion free prime ring with the right Martindale quotient ring ▫$Q$▫, ▫$L$▫ a noncentral Lie ideal of ▫$R$▫, and ▫$\delta$▫ a derivation of ▫$R$▫. Suppose that ▫$\alpha$▫ is an automorphism of ▫$R$▫, ▫$D$▫ a skew derivation of ▫$R$▫ with the associated automorphism ▫$\alpha$▫, and ▫$F$▫ a generalized skew derivation of ▫$R$▫ with the associated skew derivation ▫$D$▫. If ▫$$F(x^{m+n}) = F(x^m)x^n + x^m \delta (x^n)$$▫ is a polynomial identity for ▫$L$▫, then either ▫$R$▫ satisfies the standard polynomial identity ▫$s_4(x_1, x_2, x_3, x_4)$▫ of degree 4, or ▫$F$▫ is a generalized derivation of ▫$R$▫ and ▫$\delta = D$▫. Furthermore, in the latter case one of the following statements holds: (1) ▫$D = \delta = 0$▫ and there exists ▫$a \in Q$▫ such that ▫$F(x) = ax$▫ for all ▫$x \in R$▫; (2) ▫$\alpha$▫ is the identical mapping of ▫$R$▫. Found in: ključnih besedah Summary of found: ...mathematics, algebra, polynomial identity, generalized skew derivation, prime... Keywords: mathematics, algebra, polynomial identity, generalized skew derivation, prime ring Published: 15.10.2013; Views: 3138; Downloads: 138 Full text (0,00 KB) 
5. Qpolynomial distanceregular graphs with a [sub] 1 [equal] 0 and a [sub] 2 [not equal] 0Štefko Miklavič, 2008, original scientific article Abstract: Let ▫$\Gamma$▫ denote a ▫$Q$▫polynomial distanceregular graph with diameter ▫$D \ge 3$▫ and intersection numbers ▫$a_1=0$▫, ▫$a_2 \ne 0$▫. Let ▫$X$▫ denote the vertex set of ▫$\Gamma$▫ and let ▫$A \in {\mathrm{Mat}}_X ({\mathbb{C}})$▫ denote the adjacency matrix of ▫$\Gamma$▫. Fix ▫$x \in X$▫ and let denote $A^\ast \in {\mathrm{Mat}}_X ({\mathbb{C}})$ the corresponding dual adjacency matrix. Let ▫$T$▫ denote the subalgebra of ▫$A{\mathrm{Mat}}_X ({\mathbb{C}})$▫ generated by ▫$A$▫, ▫$A^\ast$▫. We call ▫$T$▫ the Terwilliger algebra of ▫$\Gamma$▫ with respect to ▫$x$▫. We show that up to isomorphism there exists a unique irreducible ▫$T$▫module ▫$W$▫ with endpoint 1. We show that ▫$W$▫ has dimension ▫$2D2$▫. We display a basis for ▫$W$▫ which consists of eigenvectors for ▫$A^\ast$▫. We display the action of ▫$A$▫ on this basis. We show that ▫$W$▫ appears in the standard module of ▫$\Gamma$▫ with multiplicity ▫$k1$▫, where ▫$k$▫ is the valency of ▫$\Gamma$▫. Found in: ključnih besedah Summary of found: ...mathematics, graph theory, adjacency matrix, distanceregular graph, Terwilliger... Keywords: mathematics, graph theory, adjacency matrix, distanceregular graph, Terwilliger algebra Published: 15.10.2013; Views: 3251; Downloads: 27 Full text (0,00 KB) 
6. On quartic halfarctransitive metacirculantsDragan Marušič, Primož Šparl, 2008, original scientific article Abstract: Following Alspach and Parsons, a metacirculant graph is a graph admitting a transitive group generated by two automorphisms ▫$\rho$▫ and ▫$\sigma$▫, where ▫$\rho$▫ is ▫$(m,n)$▫semiregular for some integers ▫$m \ge 1$▫, ▫$n \ge 2▫$, and where ▫$\sigma$▫ normalizes ▫$\rho$▫, cyclically permuting the orbits of ▫$\rho$▫ in such a way that ▫$\sigma^m$▫ has at least one fixed vertex. A halfarctransitive graph is a vertex and edge but not arctransitive graph. In this article quartic halfarctransitive metacirculants are explored and their connection to the so called tightly attached quartic halfarctransitive graphs is explored. It is shown that there are three essentially different possibilities for a quartic halfarctransitive metacirculant which is not tightly attached to exist. These graphs are extensively studied and some infinite families of such graphs are constructed. Found in: ključnih besedah Summary of found: ...mathematics, graph theory, metacirculant graph, halfarctransitive graph, tightly... Keywords: mathematics, graph theory, metacirculant graph, halfarctransitive graph, tightly attached, automorphism group Published: 15.10.2013; Views: 3032; Downloads: 125 Full text (0,00 KB) 
7. Consistent Cycles in 1/2ArcTransitive GraphsŠtefko Miklavič, Marko Boben, Primož Potočnik, 2009, original scientific article Found in: ključnih besedah Summary of found: ...mathematics, graph theory, 1/2arctransitivity, consistent cycle, ... Keywords: mathematics, graph theory, 1/2arctransitivity, consistent cycle Published: 15.10.2013; Views: 3504; Downloads: 35 Full text (0,00 KB) This document has more files! More...

8. Leonard triples and hypercubesŠtefko Miklavič, 2007, original scientific article Abstract: Let ▫$V$▫ denote a vector space over ▫$\mathbb{C}$▫ with finite positive dimension. By a Leonard triple on ▫$V$▫ we mean an ordered triple of linear operators on ▫$V$▫ such that for each of these operators there exists a basis of ▫$V$▫ with respect to which the matrix representing that operator is diagonal and the matrices representing the other two operators are irreducible tridiagonal. Let ▫$D$▫ denote a positive integer and let ▫${\mathcal{Q}}_D$▫ denote the graph of the ▫$D$▫dimensional hypercube. Let ▫$X$ denote the vertex set of ▫${\mathcal{Q}}_D$▫ and let ▫$A \in {\mathrm{Mat}}_X ({\mathbb{C}})$▫ denote the adjacency matrix of ▫${\mathcal{Q}}_D$▫. Fix ▫$x \in X$▫ and let ▫$A^\ast \in {\mathrm{Mat}}_X({\mathbb{C}})$▫ denote the corresponding dual adjacency matrix. Let ▫$T$▫ denote the subalgebra of ▫${\mathrm{Mat}}_X({\mathbb{C}})$ generated by ▫$A,A^\ast$▫. We refer to ▫$T$▫ as the Terwilliger algebra of ▫${\mathcal{Q}}_D$▫ with respect to ▫$x$▫. The matrices ▫$A$▫ and ▫$A^\ast$▫ are related by the fact that ▫$2iA = A^\ast A^\varepsilon  A^\varepsilon A^\ast$▫ and ▫$2iA^\ast = A^\varepsilon A  AA^\varepsilon$▫, where ▫$2iA^\varepsilon = AA^\ast  A^\ast A$▫ and ▫$i^2 = 1$▫. We show that the triple ▫$A$▫, ▫$A^\ast$▫, ▫$A^\varepsilon$▫ acts on each irreducible ▫$T$▫module as a Leonard triple. We give a detailed description of these Leonard triples. Found in: ključnih besedah Summary of found: ...mathematics, graph theory, Leonard triple, distanceregular graph, hypercube,... Keywords: mathematics, graph theory, Leonard triple, distanceregular graph, hypercube, Terwilliger algebra Published: 15.10.2013; Views: 2922; Downloads: 115 Full text (0,00 KB) 
9. On generalized Jordan triple ([alpha], [beta]) [sup] [ast]derivations and related mappingsAjda Fošner, Shakir Ali, Maja Fošner, Mohammad Salahuddin Khan, 2013, original scientific article Abstract: Let ▫$R$▫ be a 2torsion free semiprime ▫$\ast$▫ring and let ▫$\alpha, \beta$▫ be surjective endomorphisms of ▫$R$▫. The aim of the paper is to show that every generalized Jordan triple ▫$(\alpha, \beta)^\ast$▫derivation on ▫$R$▫ is a generalized Jordan ▫$(\alpha, \beta)^\ast$▫derivation. This result makes it possible to prove that every generalized Jordan triple ▫$(\alpha, \beta)^\ast$▫derivation on a semisimple ▫$H^\ast$▫algebra is a generalized Jordan ▫$(\alpha, \beta)^\ast$▫derivation. Finally, we prove that every Jordan triple left ▫$\alpha^\ast$▫centralizer on a 2torsion free semiprime ring is a Jordan left ▫$\alpha^\ast$▫centralizer. Found in: ključnih besedah Summary of found: ...mathematics, algebra, semiprime ▫$\ast$▫ring, ▫$H^\ast$▫algebra, Jordan triple ▫$(\alpha,... Keywords: mathematics, algebra, semiprime ▫$\ast$▫ring, ▫$H^\ast$▫algebra, Jordan triple ▫$(\alpha, \beta)^\ast$▫derivation, generalized Jordan triple ▫$(\alpha, \beta)^\ast$▫derivation, Jordan triple left ▫$\alpha^\ast$▫centralizer Published: 15.10.2013; Views: 2824; Downloads: 69 Full text (0,00 KB) 
10. Semiovals contained in the union of three concurrent linesIstván Kovács, György Kiss, Aart Blokhuis, Aleksander Malnič, Dragan Marušič, János Ruff, 2007, original scientific article Abstract: Semiovals which are contained in the union of three concurrent lines are studied. The notion of a strong semioval is introduced, and a complete classification of these objects in PG▫$(2,p)$▫ and PG▫$(2,p^2)$▫, ▫$p$▫ an odd prime, is given. Found in: ključnih besedah Summary of found: ...mathematics, semioval, group factorization... Keywords: mathematics, semioval, group factorization Published: 15.10.2013; Views: 2291; Downloads: 124 Full text (0,00 KB) 