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11.
Asymptotic automorphism groups of Cayley digraphs and graphs of abelian groups of prime-power order
Edward Dobson, 2010, original scientific article

Abstract: 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, ▫$G_L \triangleleft {\rm Aut}(\Gamma))$▫.
Found in: ključnih besedah
Keywords: mathematics, graph theory, Cayley graph, abelian group, automorphism group, asymptotic, ▫$p$▫-group
Published: 15.10.2013; Views: 2521; Downloads: 58
URL Full text (0,00 KB)

12.
Hamilton paths and cycles in vertex-transitive graphs of order 6p
Klavdija Kutnar, Primož Šparl, 2009, original scientific article

Abstract: 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.
Found in: ključnih besedah
Summary of found: ...graph theory, vertex-transitive, Hamilton cycle, Hamilton path, automorphism group...
Keywords: graph theory, vertex-transitive, Hamilton cycle, Hamilton path, automorphism group
Published: 15.10.2013; Views: 1676; Downloads: 14
URL Full text (0,00 KB)

13.
On cubic non-Cayley vertex-transitive graphs
Klavdija Kutnar, Dragan Marušič, Cui Zhang, 2012, original scientific article

Found in: ključnih besedah
Summary of found: ...vertex-transitive graph, non-Cayley graph, automorphism group, ...
Keywords: vertex-transitive graph, non-Cayley graph, automorphism group
Published: 15.10.2013; Views: 1270; Downloads: 63
URL Full text (0,00 KB)

14.
Hamilton cycles in (2, odd, 3)-Cayley graphs
Henry Glover, Klavdija Kutnar, Aleksander Malnič, Dragan Marušič, 2012, original scientific article

Abstract: 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.
Found in: ključnih besedah
Summary of found: ...graph, Hamilton cycle, arc-transitive graph, 1-regular action, automorphism group...
Keywords: Cayley graph, Hamilton cycle, arc-transitive graph, 1-regular action, automorphism group
Published: 15.10.2013; Views: 1249; Downloads: 60
URL Full text (0,00 KB)

15.
On cubic non-Cayley vertex-transitive graphs
Klavdija Kutnar, 2010, invited lecture at foreign university

Found in: ključnih besedah
Summary of found: ...non-Cayley, vertex-transitive, automorphism grup, ...
Keywords: non-Cayley, vertex-transitive, automorphism grup
Published: 15.10.2013; Views: 1539; Downloads: 45
URL Full text (0,00 KB)

16.
Semiregular automorphisms of arc-transitive graphs
Gabriel Verret, 2013, published scientific conference contribution abstract

Found in: ključnih besedah
Summary of found: ... automorphism group, arc-transitive graph, semiregular automorphism, ...
Keywords: automorphism group, arc-transitive graph, semiregular automorphism
Published: 15.10.2013; Views: 1729; Downloads: 21
URL Full text (0,00 KB)
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17.
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.
Found in: ključnih besedah
Summary of found: ...of ▫$X$▫ and ▫$Y$▫ in the full automorphism group of this graph. In this paper,...
Keywords: dual polar graphs, automorphism group, quadratic form, isotropic subspace
Published: 15.10.2013; Views: 1375; Downloads: 57
URL Full text (0,00 KB)

18.
On the order of arc-stabilizers in arc-transitive graphs
Gabriel Verret, 2009, published scientific conference contribution abstract

Found in: ključnih besedah
Summary of found: ...arc-transitivie graph, arc-stabilizer, automorphism group, ...
Keywords: arc-transitivie graph, arc-stabilizer, automorphism group
Published: 15.10.2013; Views: 1541; Downloads: 30
URL Full text (0,00 KB)

19.
Classification of cubic symmetric tetracirculants and pentacirculants
Boštjan Frelih, Klavdija Kutnar, 2013, original scientific article

Found in: ključnih besedah
Summary of found: ...cubic graph, symmetric, semiregular automorphism, tetracirculant, pentacirculant, ...
Keywords: cubic graph, symmetric, semiregular automorphism, tetracirculant, pentacirculant
Published: 15.10.2013; Views: 1394; Downloads: 50
URL Full text (0,00 KB)

20.
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: ...between ▫$u'$▫ and ▫$v'$▫ there exists an automorphism of the graph mapping ▫$u$▫ to ▫$u'$▫...
Keywords: distance-transitive graph, vertex-transitive graph, semiregular automorphism, permutation group
Published: 15.10.2013; Views: 1696; Downloads: 57
URL Full text (0,00 KB)

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