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51.
52.
53.
Automorphism groups of Cayley digraphs of Zp3
Edward Dobson, István Kovács, 2009, original scientific article

Keywords: Cayley digraph, automorphism group
Published in RUP: 15.10.2013; Views: 4618; Downloads: 27
URL Link to full text

54.
Arc-transitive cycle decompositions of tetravalent graphs
Štefko 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: 3531; Downloads: 85
URL Link to full text

55.
Distance-transitive graphs admit semiregular automorphisms
Klavdija Kutnar, Primož Šparl, 2010, original scientific article

Abstract: A distance-transitive graph is a graph in which for every two ordered pairs ofvertices ▫$(u,v)$▫ and ▫$(u',v')$▫ such that the distance between ▫$u$▫ and ▫$v$▫ is equal to the distance between ▫$u'$▫ and ▫$v'$▫ there exists an automorphism of the graph mapping ▫$u$▫ to ▫$u'$▫ and ▫$v$▫ to ▫$v'$▫. A semiregular element of a permutation group is anon-identity element having all cycles of equal length in its cycle decomposition. It is shown that every distance-transitive graph admits a semiregular automorphism.
Keywords: distance-transitive graph, vertex-transitive graph, semiregular automorphism, permutation group
Published in RUP: 15.10.2013; Views: 3277; Downloads: 98
URL Link to full text

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57.
On the order of arc-stabilizers in arc-transitive graphs
Gabriel Verret, 2009, published scientific conference contribution abstract

Keywords: arc-transitivie graph, arc-stabilizer, automorphism group
Published in RUP: 15.10.2013; Views: 3101; Downloads: 71
URL Link to full text

58.
On vertex-stabilizers of bipartite dual polar graphs
Štefko 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: 2801; Downloads: 123
.pdf Full text (187,79 KB)

59.
Semiregular automorphisms of arc-transitive graphs
Gabriel Verret, 2013, published scientific conference contribution abstract

Keywords: automorphism group, arc-transitive graph, semiregular automorphism
Published in RUP: 15.10.2013; Views: 3173; Downloads: 71
URL Link to full text

60.
On cubic non-Cayley vertex-transitive graphs
Klavdija Kutnar, 2010, invited lecture at foreign university

Keywords: non-Cayley, vertex-transitive, automorphism grup
Published in RUP: 15.10.2013; Views: 2866; Downloads: 81
URL Link to full text

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