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11.
Asymptotic automorphism groups of Cayley digraphs and graphs of abelian groups of prime-power order
Edward Dobson, 2010, izvirni znanstveni članek

Opis: We show that almost every Cayley graph ▫$\Gamma$▫ of an abelian group ▫$G$▫ of odd prime-power order has automorphism group as small as possible. Additionally, we show that almost every Cayley (di)graph ▫$\Gamma$▫ of an abelian group ▫$G$▫ of odd prime-power order that does not have automorphism group as small as possible is a normal Cayley (di)graph of ▫$G$▫ (that is, ▫$G_L \triangleleft {\rm Aut}(\Gamma))$▫.
Najdeno v: ključnih besedah
Ključne besede: mathematics, graph theory, Cayley graph, abelian group, automorphism group, asymptotic, ▫$p$▫-group
Objavljeno: 15.10.2013; Ogledov: 2438; Prenosov: 54
URL Polno besedilo (0,00 KB)

12.
Hamilton paths and cycles in vertex-transitive graphs of order 6p
Klavdija Kutnar, Primož Šparl, 2009, izvirni znanstveni članek

Opis: It is shown that every connected vertex-transitive graph of order ▫$6p$▫, where ▫$p$▫ is a prime, contains a Hamilton path. Moreover, it is shown that, except for the truncation of the Petersen graph, every connected vertex-transitive graph of order ▫$6p$▫ which is not genuinely imprimitive contains a Hamilton cycle.
Najdeno v: ključnih besedah
Povzetek najdenega: ...graph theory, vertex-transitive, Hamilton cycle, Hamilton path, automorphism group...
Ključne besede: graph theory, vertex-transitive, Hamilton cycle, Hamilton path, automorphism group
Objavljeno: 15.10.2013; Ogledov: 1627; Prenosov: 14
URL Polno besedilo (0,00 KB)

13.
On cubic non-Cayley vertex-transitive graphs
Klavdija Kutnar, Dragan Marušič, Cui Zhang, 2012, izvirni znanstveni članek

Najdeno v: ključnih besedah
Povzetek najdenega: ...vertex-transitive graph, non-Cayley graph, automorphism group, ...
Ključne besede: vertex-transitive graph, non-Cayley graph, automorphism group
Objavljeno: 15.10.2013; Ogledov: 1232; Prenosov: 58
URL Polno besedilo (0,00 KB)

14.
Hamilton cycles in (2, odd, 3)-Cayley graphs
Henry Glover, Klavdija Kutnar, Aleksander Malnič, Dragan Marušič, 2012, izvirni znanstveni članek

Opis: In 1969, Lovász asked if every finite, connected vertex-transitive graph has a Hamilton path. In spite of its easy formulation, no major breakthrough has been achieved thus far, and the problem is now commonly accepted to be very hard. The same holds for the special subclass of Cayley graphs where the existence of Hamilton cycles has been conjectured. In 2007, Glover and Marušič proved that a cubic Cayley graph on a finite ▫$(2, s, 3)$▫-generated group ▫$G = \langle a, x| a^2 = x^s = (ax)^3 = 1, \dots \rangle$▫ has a Hamilton path when ▫$|G|$▫ is congruent to 0 modulo 4, and has a Hamilton cycle when ▫$|G|$▫ is congruent to 2 modulo 4. The Hamilton cycle was constructed, combining the theory of Cayley maps with classical results on cyclic stability in cubic graphs, as the contractible boundary of a tree of faces in the corresponding Cayley map. With a generalization of these methods, Glover, Kutnar and Marušič in 2009 resolved the case when, apart from ▫$|G|$▫, also ▫$s$▫ is congruent to 0 modulo 4. In this article, with a further extension of the above "tree of faces" approach, a Hamilton cycle is shown to exist whenever ▫$|G|$▫ is congruent to 0 modulo 4 and s is odd. This leaves ▫$|G|$▫ congruent to 0 modulo 4 with s congruent to 2 modulo 4 as the only remaining open case. In this last case, however, the "tree of faces" approach cannot be applied, and so entirely different techniques will have to be introduced if one is to complete the proof of the existence of Hamilton cycles in cubic Cayley graphs arising from finite ▫$(2, s, 3)$▫-generated groups.
Najdeno v: ključnih besedah
Povzetek najdenega: ...graph, Hamilton cycle, arc-transitive graph, 1-regular action, automorphism group...
Ključne besede: Cayley graph, Hamilton cycle, arc-transitive graph, 1-regular action, automorphism group
Objavljeno: 15.10.2013; Ogledov: 1214; Prenosov: 56
URL Polno besedilo (0,00 KB)

15.
On cubic non-Cayley vertex-transitive graphs
Klavdija Kutnar, 2010, predavanje na tuji univerzi

Najdeno v: ključnih besedah
Povzetek najdenega: ...non-Cayley, vertex-transitive, automorphism grup, ...
Ključne besede: non-Cayley, vertex-transitive, automorphism grup
Objavljeno: 15.10.2013; Ogledov: 1497; Prenosov: 42
URL Polno besedilo (0,00 KB)

16.
Semiregular automorphisms of arc-transitive graphs
Gabriel Verret, 2013, objavljeni povzetek znanstvenega prispevka na konferenci

Najdeno v: ključnih besedah
Povzetek najdenega: ... automorphism group, arc-transitive graph, semiregular automorphism, ...
Ključne besede: automorphism group, arc-transitive graph, semiregular automorphism
Objavljeno: 15.10.2013; Ogledov: 1702; Prenosov: 21
URL Polno besedilo (0,00 KB)
Gradivo ima več datotek! Več...

17.
On vertex-stabilizers of bipartite dual polar graphs
Štefko Miklavič, 2010, izvirni znanstveni članek

Opis: 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.
Najdeno v: ključnih besedah
Povzetek najdenega: ...of ▫$X$▫ and ▫$Y$▫ in the full automorphism group of this graph. In this paper,...
Ključne besede: dual polar graphs, automorphism group, quadratic form, isotropic subspace
Objavljeno: 15.10.2013; Ogledov: 1344; Prenosov: 54
URL Polno besedilo (0,00 KB)

18.
On the order of arc-stabilizers in arc-transitive graphs
Gabriel Verret, 2009, objavljeni povzetek znanstvenega prispevka na konferenci

Najdeno v: ključnih besedah
Povzetek najdenega: ...arc-transitivie graph, arc-stabilizer, automorphism group, ...
Ključne besede: arc-transitivie graph, arc-stabilizer, automorphism group
Objavljeno: 15.10.2013; Ogledov: 1508; Prenosov: 25
URL Polno besedilo (0,00 KB)

19.
Classification of cubic symmetric tetracirculants and pentacirculants
Boštjan Frelih, Klavdija Kutnar, 2013, izvirni znanstveni članek

Najdeno v: ključnih besedah
Povzetek najdenega: ...cubic graph, symmetric, semiregular automorphism, tetracirculant, pentacirculant, ...
Ključne besede: cubic graph, symmetric, semiregular automorphism, tetracirculant, pentacirculant
Objavljeno: 15.10.2013; Ogledov: 1341; Prenosov: 46
URL Polno besedilo (0,00 KB)

20.
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: ...between ▫$u'$▫ and ▫$v'$▫ there exists an automorphism of the graph mapping ▫$u$▫ to ▫$u'$▫...
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)

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