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Keywords: pseudoline arrangement, quasiline arrangement, projective plane, incidence structure, combinatorial configuration, topological configuration, geometric configuration, sweep, wiring diagram, allowable sequence of permutations, maps on surfaces
Published in RUP: 03.01.2022; Views: 760; Downloads: 17
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Keywords: generalized bent functions, Zq-bent functions, Gray maps, (relative) difference sets, (generalized) Marioana-McFarland class, stream ciphers, filtering generator, guess and determine cryptanalysis, tap positions, (fast) algebraic attacks, algebraic immunity, derivatives, linear structures, planar mappings
Published in RUP: 09.11.2017; Views: 2526; Downloads: 57
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Keywords: varieties, Grassmanian varieties, regular maps, irreducibility
Published in RUP: 15.10.2015; Views: 2842; Downloads: 12
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Abstract: A cycle decomposition of a graph ▫$\Gamma$▫ is a set ▫$\mathcal{C}$▫ of cycles of ▫$\Gamma$▫ such that every edge of ▫$\Gamma$▫ belongs to exactly one cycle in ▫$\mathcal{C}$▫. Such a decomposition is called arc-transitive if the group of automorphisms of ▫$\Gamma$▫ that preserve setwise acts transitively on the arcs of ▫$\Gamma$▫. In this paper, we study arc-transitive cycle decompositions of tetravalent graphs. In particular, we are interested in determining and enumerating arc-transitive cycle decompositions admitted by a given arc-transitive tetravalent graph. Among other results we show that a connected tetravalent arc-transitive graph is either 2-arc-transitive, or is isomorphic to the medial graph of a reflexible map, or admits exactly one cycle structure.
Keywords: mathematics, graph theory, cycle decomposition, automorphism group, consistent cycle, medial maps
Published in RUP: 15.10.2013; Views: 3663; Downloads: 85
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