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34. Algebraični aspekti teorije grafov : doktorska disertacijaAdemir Hujdurović, 2013, doctoral dissertation Keywords: circulant, bicirculant, semiregular automorphism, vertex-transitive graph, half-arc-transitive graph, snark, Cayley graph, quasi m-Cayley graph, generalized Cayley graph, I-regular action, regular cover of a graph, automorphism group Published in RUP: 10.07.2015; Views: 3515; Downloads: 42 Link to full text |
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36. Arc-transitive cycle decompositions of tetravalent graphsŠtefko Miklavič, Primož Potočnik, Steve Wilson, 2008, original scientific article 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: 3714; Downloads: 85 Link to full text |
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39. On vertex-stabilizers of bipartite dual polar graphsŠtefko Miklavič, 2010, original scientific article Abstract: Let ▫$X,Y$▫ denote vertices of a bipartite dual polar graph, and let ▫$G_X$▫ and ▫$G_Y$▫ denote the stabilizers of ▫$X$▫ and ▫$Y$▫ in the full automorphism group of this graph. In this paper, a description of the orbits of ▫$G_X \cap G_Y$▫ in the cases when the distance between ▫$X$▫ and ▫$Y$▫ is 1 or 2, is given. Keywords: dual polar graphs, automorphism group, quadratic form, isotropic subspace Published in RUP: 15.10.2013; Views: 2894; Downloads: 124 Full text (187,79 KB) |
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