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21.
Distance-transitive graphs admit semiregular automorphisms
Klavdija Kutnar, Primož Šparl, 2010, izvirni znanstveni članek

Opis: 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.
Najdeno v: ključnih besedah
Povzetek najdenega: ...▫$v'$▫. A semiregular element of a permutation group is anon-identity element having all cycles of...
Ključne besede: distance-transitive graph, vertex-transitive graph, semiregular automorphism, permutation group
Objavljeno: 15.10.2013; Ogledov: 1642; Prenosov: 51
URL Polno besedilo (0,00 KB)

22.
Arc-transitive cycle decompositions of tetravalent graphs
Štefko Miklavič, Primož Potočnik, Stephen Wilson, 2008, izvirni znanstveni članek

Opis: 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.
Najdeno v: ključnih besedah
Povzetek najdenega: ...a decomposition is called arc-transitive if the group of automorphisms of ▫$\Gamma$▫ that preserve setwise...
Ključne besede: mathematics, graph theory, cycle decomposition, automorphism group, consistent cycle, medial maps
Objavljeno: 15.10.2013; Ogledov: 1370; Prenosov: 45
URL Polno besedilo (0,00 KB)

23.
On overgroups of regular abelian p-groups
Edward Dobson, 2009, izvirni znanstveni članek

Opis: 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.
Najdeno v: ključnih besedah
Povzetek najdenega: ...Let ▫$G$▫ be a transitive group of odd prime-power degree whose Sylow ▫$p$▫-subgroup...
Ključne besede: group theory, graph theory, Cayley graph, abelian group, regular group, p-group
Objavljeno: 15.10.2013; Ogledov: 1543; Prenosov: 58
URL Polno besedilo (0,00 KB)

24.
Distance-regular Cayley graphs on dihedral groups
Primož Potočnik, Štefko Miklavič, 2005, izvirni znanstveni članek

Opis: 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.
Najdeno v: ključnih besedah
Povzetek najdenega: ...classification of distance-regular Cayley graphs on dihedral groups. There exist four obvious families of such...
Ključne besede: mathematics, grah theory, distance-regular graph, distance-transitive graph, Cayley graph, dihedral group, dihedrant, difference set
Objavljeno: 10.07.2015; Ogledov: 847; Prenosov: 42
URL Polno besedilo (0,00 KB)

25.
Algebraični aspekti teorije grafov
Ademir Hujdurović, 2013, doktorska disertacija

Najdeno v: ključnih besedah
Povzetek najdenega: ...action, regular cover of a graph, automorphism group, ...
Ključne besede: 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
Objavljeno: 10.07.2015; Ogledov: 1534; Prenosov: 4
URL Polno besedilo (0,00 KB)

26.
Half-arc-transitive group actions with a small number of alternets
Klavdija Kutnar, 2015, objavljeni povzetek znanstvenega prispevka na konferenci

Najdeno v: ključnih besedah
Ključne besede: automorphism group, half-arc-tranistive graph, alternet
Objavljeno: 15.10.2015; Ogledov: 957; Prenosov: 9
URL Polno besedilo (0,00 KB)

27.
On the full automorphism group in vertex-transitive graphs
Dragan Marušič, 2015, objavljeni povzetek znanstvenega prispevka na konferenci

Najdeno v: ključnih besedah
Ključne besede: odd automorphism, automorphism group, graph
Objavljeno: 15.10.2015; Ogledov: 804; Prenosov: 13
URL Polno besedilo (0,00 KB)

28.
On the split structure of lifted groups
Aleksander Malnič, Rok Požar, 2016, izvirni znanstveni članek

Najdeno v: ključnih besedah
Povzetek najdenega: ...abelian cover, Cayley voltages, covering projection, graph, group extension, group presentation, lifting automorphisms, linear systems...
Ključne besede: algorithm, abelian cover, Cayley voltages, covering projection, graph, group extension, group presentation, lifting automorphisms, linear systems over the integers, semidirect product
Objavljeno: 15.10.2015; Ogledov: 989; Prenosov: 54
URL Polno besedilo (0,00 KB)

29.
Minimal normal subgroups of transitive permutation groups of square-free degree
Aleksander Malnič, Dragan Marušič, Edward Dobson, Lewis A. Nowitz, 2007, izvirni znanstveni članek

Opis: It is shown that a minimal normal subgroup of a transitive permutation group of square-free degree in its induced action is simple and quasiprimitive, with three exceptions related to ▫$A_5$▫, ▫$A_7$▫, and PSL(2,29). Moreover, it is shown that a minimal normal subgroup of a 2-closed permutation group of square-free degree in its induced action is simple. As an almost immediate consequence, it follows that a 2-closed transitive permutation group of square-free degree contains a semiregular element of prime order, thus giving a partial affirmative answer to the conjecture that all 2-closed transitive permutation groups contain such an element (see [D. Marušic, On vertex symmetric digraphs,Discrete Math. 36 (1981) 69-81; P.J. Cameron (Ed.), Problems from the fifteenth British combinatorial conference, Discrete Math. 167/168 (1997) 605-615]).
Najdeno v: ključnih besedah
Povzetek najdenega: ...It is shown that a minimal normal sub group of a transitive permutation group of square-free...
Ključne besede: mathematics, graph theory, transitive permutation group, 2-closed group, square-free degree, semiregular automorphism, vertex-transitive graph
Objavljeno: 03.04.2017; Ogledov: 854; Prenosov: 45
URL Polno besedilo (0,00 KB)

30.
Symmetry structure of bicirculants
Boštjan Frelih, Primož Šparl, Aleksander Malnič, Dragan Marušič, 2007, izvirni znanstveni članek

Opis: An ▫$n$▫-bicirculant is a graph having an automorphism with two orbits of length ▫$n$▫ and no other orbits. Symmetry properties of ▫$p$▫-bicirculants, ▫$p$▫ a prime, are extensively studied. In particular, the actions of their automorphism groups are described in detail in terms of certain algebraic representation of such graphs.
Najdeno v: ključnih besedah
Ključne besede: mathematics, graph theory, graph, circulant, bicirculant, automorphism group
Objavljeno: 03.04.2017; Ogledov: 959; Prenosov: 50
URL Polno besedilo (0,00 KB)

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