21. A note on generalized (m,n)-Jordan centralizersAjda Fošner, 2013, izvirni znanstveni članek Opis: The aim of this paper is to define generalized ▫$(m, n)$▫-Jordan centralizers and to prove that on a prime ring with nonzero center and ▫${\rm char}(R) \ne 6mn(m+n)(m+2n)$▫ every generalized ▫$(m, n)$▫-Jordan centralizer is a two-sided centralizer.
Ključne besede: mathematics, prime ring, semiprime ring, left (right) centralizer, left (right) Jordan centralizer, (m, n)-Jordan centralizer, generalized (m, n)-Jordan centralizer
Objavljeno v RUP: 15.10.2013; Ogledov: 3584; Prenosov: 170
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22. Hyers-Ulam-Rassias stability of generalized module left (m,n)-derivationsAjda Fošner, 2013, izvirni znanstveni članek Opis: The generalized Hyers-Ulam-Rassias stability of generalized module left ▫$(m,n)$▫-derivations on a normed algebra ▫$\mathcal{A}$▫ into a Banach left ▫$\mathcal{A}$▫-module is established.
Ključne besede: Hyers-Ulam-Rassias stability, normed algebra, Banach left A-module, module left (m, n)-derivation, generalized module left (m, n)-derivation
Objavljeno v RUP: 15.10.2013; Ogledov: 3487; Prenosov: 107
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24. On the generalized Hyers-Ulam stability of module left (m, n)-derivationsAjda Fošner, 2012, izvirni znanstveni članek Opis: We study the generalized Hyers-Ulam stability of functional equations of module left ▫$(m, n)$▫-derivations.
Ključne besede: mathematics, algebra, generalized Hyers-Ulam stability, normed algebra, Banach left A-module, module left ▫$(m, n)$▫-derivation
Objavljeno v RUP: 15.10.2013; Ogledov: 3575; Prenosov: 131
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25. The strongly distance-balanced property of the generalized Petersen graphsKlavdija Kutnar, Aleksander Malnič, Dragan Marušič, Štefko Miklavič, 2009, izvirni znanstveni članek Opis: A graph ▫$X$▫ is said to be strongly distance-balanced whenever for any edge ▫$uv$▫ of ▫$X$▫ and any positive integer ▫$i$▫, the number of vertices at distance ▫$i$▫ from ▫$u$▫ and at distance ▫$i + 1$▫ from ▫$v$▫ is equal to the number of vertices at distance ▫$i + 1$▫ from ▫$u$▫ and at distance ▫$i$▫ from ▫$v$▫. It is proven that for any integers ▫$k \ge 2$▫ and ▫$n \ge k^2 + 4k + 1$▫, the generalized Petersen graph GP▫$(n, k)$▫ is not strongly distance-balanced.
Ključne besede: graph, strongy distance-balanced, generalized Petersen graph
Objavljeno v RUP: 15.10.2013; Ogledov: 3142; Prenosov: 132
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26. On generalized Jordan triple ([alpha], [beta]) [sup] [ast]-derivations and related mappingsShakir Ali, Ajda Fošner, Maja Fošner, Mohammad Salahuddin Khan, 2013, izvirni znanstveni članek Opis: Let ▫$R$▫ be a 2-torsion 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 2-torsion free semiprime ring is a Jordan left ▫$\alpha^\ast$▫-centralizer.
Ključne besede: 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
Objavljeno v RUP: 15.10.2013; Ogledov: 4459; Prenosov: 77
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27. Identities with generalized skew derivations on Lie idealsVincenzo De Filippis, Ajda Fošner, Feng Wei, 2013, izvirni znanstveni članek Opis: Let ▫$m, n$▫ be two nonzero fixed positive integers, ▫$R$▫ a 2-torsion free prime ring with the right Martindale quotient ring ▫$Q$▫, ▫$L$▫ a non-central 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 ▫$R$▫.
Ključne besede: mathematics, algebra, polynomial identity, generalized skew derivation, prime ring
Objavljeno v RUP: 15.10.2013; Ogledov: 4183; Prenosov: 144
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28. Distance-balanced graphs: Symmetry conditionsKlavdija Kutnar, Aleksander Malnič, Dragan Marušič, Štefko Miklavič, 2006, izvirni znanstveni članek Opis: A graph ▫$X$▫ is said to be distance-balanced if for any edge ▫$uv$▫ of ▫$X$▫, the number of vertices closer to ▫$u$▫ than to ▫$v$▫ is equal to the number of vertices closer to ▫$v$▫ than to ▫$u$▫. A graph ▫$X$▫ is said to be strongly distance-balanced if for any edge ▫$uv$▫ of ▫$X$▫ and any integer ▫$k$▫, the number of vertices at distance ▫$k$▫ from ▫$u$▫ and at distance ▫$k+1$▫ from ▫$v$▫ is equal to the number of vertices at distance ▫$k+1$▫ from ▫$u$▫ and at distance ▫$k$▫ from ▫$v$▫. Exploring the connection between symmetry properties of graphs and the metric property of being (strongly) distance-balanced is the main theme of this article. That a vertex-transitive graph is necessarily strongly distance-balanced and thus also distance-balanced is an easy observation. With only a slight relaxation of the transitivity condition, the situation changes drastically: there are infinite families of semisymmetric graphs (that is, graphs which are edge-transitive, but not vertex-transitive) which are distance-balanced, but there are also infinite families of semisymmetric graphs which are not distance-balanced. Results on the distance-balanced property in product graphs prove helpful in obtaining these constructions. Finally, a complete classification of strongly distance-balanced graphs is given for the following infinite families of generalized Petersen graphs: GP▫$(n,2)$▫, GP▫$(5k+1,k)$▫, GP▫$(3k 3,k)$▫, and GP▫$(2k+2,k)$▫.
Ključne besede: graph theory, graph, distance-balanced graphs, vertex-transitive, semysimmetric, generalized Petersen graph
Objavljeno v RUP: 15.10.2013; Ogledov: 4453; Prenosov: 90
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30. Isomorphism checking of I-graphsBoris Horvat, Tomaž Pisanski, Arjana Žitnik, 2012, izvirni znanstveni članek Opis: 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 non-isomorphic ▫$I$▫-graphs and unit-distance representations of generalized Petersen graphs.
Ključne besede: mathematics, graph theory, isomorphism, I-graph, generalized Petersen graph
Objavljeno v RUP: 15.10.2013; Ogledov: 4166; Prenosov: 136
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