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11.
On generalized Cayley graphs
Klavdija Kutnar, 2013, objavljeni povzetek znanstvenega prispevka na konferenci

Najdeno v: ključnih besedah
Povzetek najdenega: ...vertex-transitive, bicirculant, generalized Cayley graph, ...
Ključne besede: vertex-transitive, bicirculant, generalized Cayley graph
Objavljeno: 15.10.2013; Ogledov: 1993; Prenosov: 11
URL Polno besedilo (0,00 KB)

12.
Quasi m-Cayley circulants
Ademir Hujdurović, 2013, objavljeni znanstveni prispevek na konferenci

Opis: A graph ▫$\Gamma$▫ is called a quasi ▫$m$▫-Cayley graph on a group ▫$G$▫ if there exists a vertex ▫$\infty \in V(\Gamma)$▫ and a subgroup ▫$G$▫ of the vertex stabilizer ▫$\text{Aut}(\Gamma)_\infty$▫ of the vertex ▫$\infty$▫ in the full automorphism group ▫$\text{Aut}(\Gamma)$▫ of ▫$\Gamma$▫, such that ▫$G$▫ acts semiregularly on ▫$V(\Gamma) \setminus \{\infty\}$▫ with ▫$m$▫ orbits. If the vertex ▫$\infty$▫ is adjacent to only one orbit of ▫$G$▫ on ▫$V(\Gamma) \setminus \{\infty\}$▫, then ▫$\Gamma$▫ is called a strongly quasi ▫$m$▫-Cayley graph on ▫$G$▫ .In this paper complete classifications of quasi 2-Cayley, quasi 3-Cayley and strongly quasi 4-Cayley connected circulants are given.
Najdeno v: ključnih besedah
Povzetek najdenega: ...A graph ▫$\Gamma$▫ is called a quasi ▫$m$▫-Cayley graph...
Ključne besede: arc-transitive, circulant, quasi m-Cayley graph
Objavljeno: 15.10.2013; Ogledov: 1809; Prenosov: 65
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: 1349; Prenosov: 70
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: ...Lovász asked if every finite, connected vertex-transitive graph has a Hamilton path. In spite of...
Ključne besede: Cayley graph, Hamilton cycle, arc-transitive graph, 1-regular action, automorphism group
Objavljeno: 15.10.2013; Ogledov: 1295; Prenosov: 68
URL Polno besedilo (0,00 KB)

15.
Hamilton cycle and Hamilton path extendability of Cayley graphs on abelian groups
Štefko Miklavič, Primož Šparl, 2012, izvirni znanstveni članek

Opis: In this paper the concepts of Hamilton cycle (HC) and Hamilton path (HP) extendability are introduced. A connected graph ▫$\Gamma$▫ is ▫$n$▫-HC-extendable if it contains a path of length ▫$n$▫ and if every such path is contained in some Hamilton cycle of ▫$\Gamma$▫. Similarly, ▫$\Gamma$▫ is weakly ▫$n$▫-HP-extendable if it contains a path of length ▫$n$▫ and if every such path is contained in some Hamilton path of ▫$\Gamma$▫. Moreover, ▫$\Gamma$▫ is strongly ▫$n$▫-HP-extendable if it contains a path of length ▫$n$▫ and if for every such path $P$ there is a Hamilton path of ▫$\Gamma$▫ starting with ▫$P$▫. These concepts are then studied for the class of connected Cayley graphs on abelian groups. It is proved that every connected Cayley graph on an abelian group of order at least three is 2-HC-extendable and a complete classification of 3-HC-extendable connected Cayley graphs of abelian groups is obtained. Moreover, it is proved that every connected Cayley graph on an abelian group of order at least five is weakly 4-HP-extendable.
Najdeno v: ključnih besedah
Povzetek najdenega: ...path (HP) extendability are introduced. A connected graph ▫$\Gamma$▫ is ▫$n$▫-HC-extendable if it contains a...
Ključne besede: graph theory, Hamilton cycle, Hamilton path, n-HC-extendable, strongly n-HP-extendable, weakly n-HP-extendable, Cayley graph, abelian group
Objavljeno: 15.10.2013; Ogledov: 1320; Prenosov: 82
URL Polno besedilo (0,00 KB)

16.
Cubic Cayley graphs and snarks
Klavdija Kutnar, Ademir Hujdurović, Dragan Marušič, 2012, objavljeni povzetek znanstvenega prispevka na konferenci (vabljeno predavanje)

Najdeno v: ključnih besedah
Povzetek najdenega: ...Cayley graph, snark, arc-transitive graph, Cayley map, ...
Ključne besede: Cayley graph, snark, arc-transitive graph, Cayley map
Objavljeno: 15.10.2013; Ogledov: 1331; Prenosov: 51
URL Polno besedilo (0,00 KB)

17.
Special issue of discrete mathematics on Hamiltonicity problem for vertex-transitive (Cayley) graphs
Dragan Marušič, 2009, predgovor, spremna beseda

Najdeno v: ključnih besedah
Povzetek najdenega: ...Hamilton cycle, Hamilton path, Vetrex-transitive graph, Cayley graph, ...
Ključne besede: Hamilton cycle, Hamilton path, Vetrex-transitive graph, Cayley graph
Objavljeno: 15.10.2013; Ogledov: 1420; Prenosov: 14
URL Polno besedilo (0,00 KB)

18.
Hamiltonian cycles in Cayley graphs whose order has few prime factors
Klavdija Kutnar, Dragan Marušič, D. W. Morris, Joy Morris, Primož Šparl, 2012, izvirni znanstveni članek

Opis: We prove that if Cay▫$(G; S)$▫ is a connected Cayley graph with ▫$n$▫ vertices, and the prime factorization of ▫$n$▫ is very small, then Cay▫$(G; S)$▫ has a hamiltonian cycle. More precisely, if ▫$p$▫, ▫$q$▫, and ▫$r$▫ are distinct primes, then ▫$n$▫ can be of the form kp with ▫$24 \ne k < 32$▫, or of the form ▫$kpq$▫ with ▫$k \le 5$▫, or of the form ▫$pqr$▫, or of the form ▫$kp^2$▫ with ▫$k \le 4$▫, or of the form ▫$kp^3$▫ with ▫$k \le 2$▫.
Najdeno v: ključnih besedah
Povzetek najdenega: ...if Cay▫$(G; S)$▫ is a connected Cayley graph with ▫$n$▫ vertices, and the prime factorization...
Ključne besede: graph theory, Cayley graphs, hamiltonian cycles
Objavljeno: 15.10.2013; Ogledov: 1681; Prenosov: 69
URL Polno besedilo (0,00 KB)

19.
A note on a geometric construction of large Cayley graps of given degree and diameter
György Kiss, István Kovács, Klavdija Kutnar, János Ruff, Primož Šparl, 2008, objavljeni povzetek znanstvenega prispevka na konferenci

Najdeno v: ključnih besedah
Povzetek najdenega: ...diameter-degree problem, Cayley graph, projective space, ...
Ključne besede: diameter-degree problem, Cayley graph, projective space
Objavljeno: 15.10.2013; Ogledov: 1821; Prenosov: 12
URL Polno besedilo (0,00 KB)

20.
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: ...determine the full automorphism group of a Cayley diagraph of an abelian group with rank...
Ključne besede: group theory, graph theory, Cayley graph, abelian group, regular group, p-group
Objavljeno: 15.10.2013; Ogledov: 1643; Prenosov: 74
URL Polno besedilo (0,00 KB)

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