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31.
A note on finite non-solvable groups with few non-cyclic subgroups
Jiangtao Shi, Cui Zhang, 2011, original scientific article

Found in: ključnih besedah
Summary of found: ...finite group, non-cyclic subgroup, non-solvable group, ...
Keywords: finite group, non-cyclic subgroup, non-solvable group
Published: 15.10.2013; Views: 1144; Downloads: 18
URL Full text (0,00 KB)

32.
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.
Found in: ključnih besedah
Summary of found: ...▫$v'$▫. A semiregular element of a permutation group is anon-identity element having all cycles of...
Keywords: distance-transitive graph, vertex-transitive graph, semiregular automorphism, permutation group
Published: 15.10.2013; Views: 1634; Downloads: 51
URL Full text (0,00 KB)

33.
Arc-transitive cycle decompositions of tetravalent graphs
Štefko 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: ...a decomposition is called arc-transitive if the group of automorphisms of ▫$\Gamma$▫ that preserve setwise...
Keywords: mathematics, graph theory, cycle decomposition, automorphism group, consistent cycle, medial maps
Published: 15.10.2013; Views: 1360; Downloads: 44
URL Full text (0,00 KB)

34.
Automorphism groups of Cayley digraphs of Zp3
Edward Dobson, István Kovács, 2009, original scientific article

Found in: ključnih besedah
Summary of found: ...Cayley digraph, automorphism group, ...
Keywords: Cayley digraph, automorphism group
Published: 15.10.2013; Views: 2213; Downloads: 8
URL Full text (0,00 KB)
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35.
On overgroups of regular abelian p-groups
Edward 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: ...Let ▫$G$▫ be a transitive group of odd prime-power degree whose Sylow ▫$p$▫-subgroup...
Keywords: group theory, graph theory, Cayley graph, abelian group, regular group, p-group
Published: 15.10.2013; Views: 1536; Downloads: 57
URL Full text (0,00 KB)

36.
Distance-regular Cayley graphs on dihedral groups
Primož 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: ...classification of distance-regular Cayley graphs on dihedral groups. There exist four obvious families of such...
Keywords: mathematics, grah theory, distance-regular graph, distance-transitive graph, Cayley graph, dihedral group, dihedrant, difference set
Published: 10.07.2015; Views: 841; Downloads: 42
URL Full text (0,00 KB)

37.
Algebraični aspekti teorije grafov
Ademir Hujdurović, 2013, doctoral dissertation

Found in: ključnih besedah
Summary of found: ...action, regular cover of a graph, automorphism group, ...
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: 1525; Downloads: 4
URL Full text (0,00 KB)

38.
Nilpotent 3-BCI groups
István Kovács, Sergio Hiroki Koike Quintanar, 2014, published scientific conference contribution abstract

Found in: ključnih besedah
Summary of found: ... group, nilpotent, BCI, ...
Keywords: group, nilpotent, BCI
Published: 15.10.2015; Views: 903; Downloads: 10
URL Full text (0,00 KB)

39.
Classification of regular maps of Euler characteristic -3p
Marston D. E. Conder, Roman Nedela, Jozef Širan, 2012, original scientific article

Found in: ključnih besedah
Summary of found: ...grupa avtomorfizmov, Eulerjeva karakteristika, regular map, automorphism group, Euler characteristics, ...
Keywords: regularen zemljevid, grupa avtomorfizmov, Eulerjeva karakteristika, regular map, automorphism group, Euler characteristics
Published: 15.10.2015; Views: 1115; Downloads: 59
URL Full text (0,00 KB)

40.
Half-arc-transitive group actions with a small number of alternets
Klavdija Kutnar, 2015, published scientific conference contribution abstract

Found in: ključnih besedah
Keywords: automorphism group, half-arc-tranistive graph, alternet
Published: 15.10.2015; Views: 952; Downloads: 9
URL Full text (0,00 KB)

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