31. |
32. |
33. Arc-transitive cycle decompositions of tetravalent graphsŠtefko Miklavič, Primož Potočnik, Stephen 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. Found in: ključnih besedah Summary of found: ...... Keywords: mathematics, graph theory, cycle decomposition, automorphism group, consistent cycle, medial maps Published: 15.10.2013; Views: 1369; Downloads: 44 Full text (0,00 KB) |
34. |
35. On overgroups of regular abelian p-groupsEdward Dobson, 2009, original scientific article Abstract: Let ▫$G$▫ be a transitive group of odd prime-power degree whose Sylow ▫$p$▫-subgroup ▫$P$▫ is abelian od rank ▫$t$▫. Weshow that if ▫$p > 2^{t-1}$▫, then ▫$G$▫ has a normal subgroup that is a direct product of ▫$t$▫ permutation groups of smaller degree that are either cyclic or doubly-transitive simple groups. As a consequence, we determine the full automorphism group of a Cayley diagraph of an abelian group with rank two such that the Sylow ▫$p$▫-subgroup of the full automorphism group is abelian. Found in: ključnih besedah Summary of found: ...... Keywords: group theory, graph theory, Cayley graph, abelian group, regular group, p-group Published: 15.10.2013; Views: 1541; Downloads: 57 Full text (0,00 KB) |
36. Distance-regular Cayley graphs on dihedral groupsPrimož Potočnik, Štefko Miklavič, 2005, original scientific article Abstract: The main result of this article is a classification of distance-regular Cayley graphs on dihedral groups. There exist four obvious families of such graphs, which are called trivial. These are: complete graphs, complete bipartite graphs, complete bipartite graphs with the edges of a 1-factor removed, and cycles. It is proved that every non-trivial distance-regular Cayley graph on a dihedral group is bipartite, non-antipodal, has diameter 3 and arises either from a cyclic di#erence set, or possibly (if any such exists) from a dihedral difference set satisfying some additional conditions. Finally, all distance-transitive Cayley graphs on dihedral groups are determined. It transpires that a Cayley graph on a dihedral group is distance-transitive if and only if it is trivial, or isomorphic to the incidence or to the non-incidence graph of a projective space ▫$\mathrm{PG}_{d-1} (d,q)$▫, ▫$d \ge 2$▫, or the unique pair of complementary symmetric designs on 11 vertices. Found in: ključnih besedah Summary of found: ...... Keywords: mathematics, grah theory, distance-regular graph, distance-transitive graph, Cayley graph, dihedral group, dihedrant, difference set Published: 10.07.2015; Views: 847; Downloads: 42 Full text (0,00 KB) |
37. Algebraični aspekti teorije grafovAdemir Hujdurović, 2013, doctoral dissertation Found in: ključnih besedah Summary of found: ...... 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: 10.07.2015; Views: 1532; Downloads: 4 Full text (0,00 KB) |
38. |
39. Classification of regular maps of Euler characteristic -3pMarston D. E. Conder, Roman Nedela, Jozef Širan, 2012, original scientific article Found in: ključnih besedah Summary of found: ...... Keywords: regularen zemljevid, grupa avtomorfizmov, Eulerjeva karakteristika, regular map, automorphism group, Euler characteristics Published: 15.10.2015; Views: 1116; Downloads: 59 Full text (0,00 KB) |
40. |