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1.
Hamilton paths in vertex-transitive graphs of order 10p
Klavdija Kutnar, Dragan Marušič, Cui Zhang, 2012, izvirni znanstveni članek

Opis: It is shown that every connected vertex-transitive graph of order ▫$10p$▫, ▫$p \ne 7$▫ a prime, which is not isomorphic to a quasiprimitive graph arising from the action of PSL▫$(2,k)$▫ on cosets of ▫$\mathbb{Z}_k \times \mathbb{Z}_{(k-1)/10}$▫, contains a Hamilton path.
Najdeno v: ključnih besedah
Povzetek najdenega: ...It is shown that every connected vertex-transitive graph of order ▫$10p$▫, ▫$p \ne 7$▫ a... ...graph, vertex-transitive, Hamilton cycle, Hamilton path, automorphism group...
Ključne besede: graph, vertex-transitive, Hamilton cycle, Hamilton path, automorphism group
Objavljeno: 15.10.2013; Ogledov: 1774; Prenosov: 12
URL Polno besedilo (0,00 KB)

2.
On prime-valent symmetric bicirculants and Cayley snarks
Ademir Hujdurović, Klavdija Kutnar, Dragan Marušič, 2013, objavljeni znanstveni prispevek na konferenci

Najdeno v: ključnih besedah
Povzetek najdenega: ... graph, Cayley graph, arc-transitive, snark, semiregular automorphism, bicirculant,...
Ključne besede: graph, Cayley graph, arc-transitive, snark, semiregular automorphism, bicirculant
Objavljeno: 15.10.2013; Ogledov: 1631; Prenosov: 81
URL Polno besedilo (0,00 KB)

3.
Hamiltonicity of vertex-transitive graphs of order 4p
Klavdija Kutnar, Dragan Marušič, 2008, izvirni znanstveni članek

Opis: It is shown that every connected vertex-transitive graph of order ▫$4p$▫, where ▫$p$▫ is a prime, is hamiltonian with the exception of the Coxeter graph which is known to possess a Hamilton path.
Najdeno v: ključnih besedah
Povzetek najdenega: ...It is shown that every connected vertex-transitive graph of order ▫$4p$▫, where ▫$p$▫ is a... ...graph theory, vertex-transitive graphs, Hamilton cycle, automorphism group...
Ključne besede: graph theory, vertex-transitive graphs, Hamilton cycle, automorphism group
Objavljeno: 15.10.2013; Ogledov: 1650; Prenosov: 18
URL Polno besedilo (0,00 KB)

4.
The full automorphism group of Cayley graphs of ${mathbb Z}_ptimes{mathbbZ}_{p^2}$
Edward Dobson, 2012, izvirni znanstveni članek

Najdeno v: ključnih besedah
Povzetek najdenega: ...Cayley graph, abelian group, automorphism group, ...
Ključne besede: Cayley graph, abelian group, automorphism group
Objavljeno: 15.10.2013; Ogledov: 1809; Prenosov: 35
URL Polno besedilo (0,00 KB)

5.
On quartic half-arc-transitive metacirculants
Dragan Marušič, Primož Šparl, 2008, izvirni znanstveni članek

Opis: Following Alspach and Parsons, a metacirculant graph is a graph admitting a transitive group generated by two automorphisms ▫$\rho$▫ and ▫$\sigma$▫, where ▫$\rho$▫ is ▫$(m,n)$▫-semiregular for some integers ▫$m \ge 1$▫, ▫$n \ge 2▫$, and where ▫$\sigma$▫ normalizes ▫$\rho$▫, cyclically permuting the orbits of ▫$\rho$▫ in such a way that ▫$\sigma^m$▫ has at least one fixed vertex. A half-arc-transitive graph is a vertex- and edge- but not arc-transitive graph. In this article quartic half-arc-transitive metacirculants are explored and their connection to the so called tightly attached quartic half-arc-transitive graphs is explored. It is shown that there are three essentially different possibilities for a quartic half-arc-transitive metacirculant which is not tightly attached to exist. These graphs are extensively studied and some infinite families of such graphs are constructed.
Najdeno v: ključnih besedah
Povzetek najdenega: ...Following Alspach and Parsons, a metacirculant graph is a graph admitting a transitive group... ...theory, metacirculant graph, half-arc-transitive graph, tightly attached, automorphism group...
Ključne besede: mathematics, graph theory, metacirculant graph, half-arc-transitive graph, tightly attached, automorphism group
Objavljeno: 15.10.2013; Ogledov: 1733; Prenosov: 68
URL Polno besedilo (0,00 KB)

6.
The full automorphism group of a Cayley graph
Gabriel Verret, 2013, objavljeni povzetek znanstvenega prispevka na konferenci (vabljeno predavanje)

Najdeno v: ključnih besedah
Ključne besede: automorphism group, Cayley graph
Objavljeno: 15.10.2013; Ogledov: 2332; Prenosov: 21
URL Polno besedilo (0,00 KB)
Gradivo ima več datotek! Več...

7.
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
Povzetek najdenega: ...We show that almost every Cayley graph ▫$\Gamma$▫ of an abelian group ▫$G$▫ of...
Ključne besede: mathematics, graph theory, Cayley graph, abelian group, automorphism group, asymptotic, ▫$p$▫-group
Objavljeno: 15.10.2013; Ogledov: 2573; Prenosov: 62
URL Polno besedilo (0,00 KB)

8.
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: ...It is shown that every connected vertex-transitive graph of order ▫$6p$▫, where ▫$p$▫ is a... ...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: 1711; Prenosov: 14
URL Polno besedilo (0,00 KB)

9.
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: 1307; Prenosov: 67
URL Polno besedilo (0,00 KB)

10.
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: ...Lovász asked if every finite, connected vertex-transitive graph has a Hamilton path. In spite of... ...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: 1277; Prenosov: 63
URL Polno besedilo (0,00 KB)

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