1. 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 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 ▫$R$▫.
Found in: osebi
Keywords: mathematics, algebra, polynomial identity, generalized skew derivation, prime ring
Published: 15.10.2013; Views: 3139; Downloads: 138
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2. On 2-fold covers of graphsKlavdija Kutnar, Yan-Quan Feng, Aleksander Malnič, Dragan Marušič, 2008, original scientific article Abstract: A regular covering projection ▫$\wp : \widetilde{X} \to X$▫ of connected graphs is ▫$G$▫-admissible if ▫$G$▫ lifts along ▫$\wp$▫. Denote by ▫$\tilde{G}$▫ the lifted group, and let CT▫$(\wp)$▫ be the group of covering transformations. The projection is called ▫$G$▫-split whenever the extension ▫{$\mathrm{CT}}(\wp) \to \tilde{G} \to G$▫ splits. In this paper, split 2-covers are considered, with a particular emphasis given to cubic symmetric graphs. Supposing that ▫$G$▫ is transitive on ▫$X$▫, a ▫$G$▫-split cover is said to be ▫$G$▫-split-transitive if all complements ▫$\tilde{G} \cong G$▫ of CT▫$(\wp)$▫ within ▫$\tilde{G}$▫ are transitive on ▫$\widetilde{X}$▫; it is said to be ▫$G$▫-split-sectional whenever for each complement ▫$\tilde{G}$▫ there exists a ▫$\tilde{G}$▫-invariant section of ▫$\wp$▫; and it is called ▫$G$▫-split-mixed otherwise. It is shown, when ▫$G$▫ is an arc-transitive group, split-sectional and split-mixed 2-covers lead to canonical double covers. Split-transitive covers, however, are considerably more difficult to analyze. For cubic symmetric graphs split 2-cover are necessarily canonical double covers (that is, no ▫$G$▫-split-transitive 2-covers exist) when ▫$G$▫ is 1-regular or 4-regular. In all other cases, that is, if ▫$G$▫ is ▫$s$▫-regular, ▫$s=2,3$▫ or ▫$5$▫, a necessary and sufficient condition for the existence of a transitive complement ▫$\tilde{G}$▫ is given, and moreover, an infinite family of split-transitive 2-covers based on the alternating groups of the form ▫$A_{12k+10}$▫ is constructed. Finally, chains of consecutive 2-covers, along which an arc-transitive group ▫$G$▫ has successive lifts, are also considered. It is proved that in such a chain, at most two projections can be split. Further, it is shown that, in the context of cubic symmetric graphs, if exactly two of them are split, then one is split-transitive and the other one is either split-sectional or split-mixed.
Found in: osebi
Keywords: graph theory, graphs, cubic graphs, symmetric graphs, ▫$s$▫-regular group, regular covering projection
Published: 15.10.2013; Views: 2673; Downloads: 31
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4. Quasi-semiregular automorphisms of cubic and tetravalent arc-transitive graphsKlavdija Kutnar, Ademir Hujdurović, Dragan Marušič, Yan-Quan Feng, István Kovács, 2018, unpublished conference contribution Found in: osebi
Keywords: quasi-semiregular automorphism, cubic graph, tetravalent graph, arc-transitive graph
Published: 06.12.2018; Views: 1363; Downloads: 123
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5. Quasi-semiregular automorphisms of cubic and tetravalent arc-transitive graphsKlavdija Kutnar, István Kovács, Dragan Marušič, Ademir Hujdurović, Yan-Quan Feng, 2019, original scientific article Found in: osebi
Keywords: cubic graph, tetravalent graph, arc-transitive, quasi-semiregular automorphism
Published: 14.03.2019; Views: 1049; Downloads: 248
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10. The signless Laplacian spectral radius of bounded degree graphs on surfacesLihua Feng, Guihai Yu, Aleksandar Ilić, Dragan Stevanović, 2015, original scientific article Found in: osebi
Keywords: signless Laplacian matrix, spectral radius, Euler genus, outerplanar graph, Halin graph
Published: 03.04.2017; Views: 1796; Downloads: 146
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