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21.
Construction of Hamilton cycles in (2,s,3)-Cayley graphs
Klavdija Kutnar, 2010, objavljeni povzetek znanstvenega prispevka na konferenci

Najdeno v: osebi
Ključne besede: Hamilton cycle, Cayley graph
Objavljeno: 15.10.2013; Ogledov: 1278; Prenosov: 8
URL Polno besedilo (0,00 KB)

22.
On 2-fold covers of graphs
Yan-Quan Feng, Klavdija Kutnar, Aleksander Malnič, Dragan Marušič, 2008, izvirni znanstveni članek

Opis: A regular covering projection ▫$\wp : \widetilde{X} \to X$▫ of connected graphs is ▫$G$▫-admissible if ▫$G$▫ lifts along ▫$\wp$▫. Denote by ▫$\tilde{G}$▫ the lifted group, and let CT▫$(\wp)$▫ be the group of covering transformations. The projection is called ▫$G$▫-split whenever the extension ▫{$\mathrm{CT}}(\wp) \to \tilde{G} \to G$▫ splits. In this paper, split 2-covers are considered, with a particular emphasis given to cubic symmetric graphs. Supposing that ▫$G$▫ is transitive on ▫$X$▫, a ▫$G$▫-split cover is said to be ▫$G$▫-split-transitive if all complements ▫$\tilde{G} \cong G$▫ of CT▫$(\wp)$▫ within ▫$\tilde{G}$▫ are transitive on ▫$\widetilde{X}$▫; it is said to be ▫$G$▫-split-sectional whenever for each complement ▫$\tilde{G}$▫ there exists a ▫$\tilde{G}$▫-invariant section of ▫$\wp$▫; and it is called ▫$G$▫-split-mixed otherwise. It is shown, when ▫$G$▫ is an arc-transitive group, split-sectional and split-mixed 2-covers lead to canonical double covers. Split-transitive covers, however, are considerably more difficult to analyze. For cubic symmetric graphs split 2-cover are necessarily canonical double covers (that is, no ▫$G$▫-split-transitive 2-covers exist) when ▫$G$▫ is 1-regular or 4-regular. In all other cases, that is, if ▫$G$▫ is ▫$s$▫-regular, ▫$s=2,3$▫ or ▫$5$▫, a necessary and sufficient condition for the existence of a transitive complement ▫$\tilde{G}$▫ is given, and moreover, an infinite family of split-transitive 2-covers based on the alternating groups of the form ▫$A_{12k+10}$▫ is constructed. Finally, chains of consecutive 2-covers, along which an arc-transitive group ▫$G$▫ has successive lifts, are also considered. It is proved that in such a chain, at most two projections can be split. Further, it is shown that, in the context of cubic symmetric graphs, if exactly two of them are split, then one is split-transitive and the other one is either split-sectional or split-mixed.
Najdeno v: osebi
Ključne besede: graph theory, graphs, cubic graphs, symmetric graphs, ▫$s$▫-regular group, regular covering projection
Objavljeno: 15.10.2013; Ogledov: 1191; Prenosov: 13
URL Polno besedilo (0,00 KB)

23.
Recent trends and future directions in vertex-transitive graphs
Klavdija Kutnar, Dragan Marušič, 2008, izvirni znanstveni članek

Opis: A graph is said to be vertex-transitive if its automorphism group acts transitively on the vertex set. Some recent developments and possible future directions regarding two famous open problems, asking about existence of Hamilton paths and existence of semiregular automorphisms in vertex-transitive graphs, are discussed, together with some recent results on arc-transitive graphs and half-arc-transitive graphs, two special classes of vertex-transitive graphs that have received particular attention over the last decade.
Najdeno v: osebi
Ključne besede: matematika, teorija grafov, tranzitivni grafi, poltranzitivni grafi, Hamiltonov cikel, delovanje grupe, polregularna grupa
Objavljeno: 15.10.2013; Ogledov: 1478; Prenosov: 53
URL Polno besedilo (0,00 KB)

24.
On generalized Cayley graphs
Klavdija Kutnar, 2013, objavljeni povzetek znanstvenega prispevka na konferenci

Najdeno v: osebi
Ključne besede: vertex-transitive, bicirculant, generalized Cayley graph
Objavljeno: 15.10.2013; Ogledov: 1845; Prenosov: 11
URL Polno besedilo (0,00 KB)

25.
Fullerenes via their automorphism groups
Klavdija Kutnar, Dragan Marušič, Dušanka Janežič, 2010, izvirni znanstveni članek

Najdeno v: osebi
Ključne besede: matematika, morfologija, avtomorfizem, fulereni
Objavljeno: 15.10.2013; Ogledov: 1643; Prenosov: 12
URL Polno besedilo (0,00 KB)

26.
On cubic symmetric graphs of girth 6
Klavdija Kutnar, 2007, predavanje na tuji univerzi

Najdeno v: osebi
Objavljeno: 15.10.2013; Ogledov: 1868; Prenosov: 13
URL Polno besedilo (0,00 KB)

27.
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: osebi
Ključne besede: graph theory, vertex-transitive, Hamilton cycle, Hamilton path, automorphism group
Objavljeno: 15.10.2013; Ogledov: 1601; Prenosov: 14
URL Polno besedilo (0,00 KB)

28.
Classification of half-arc-transitive graphs of order 4p
Klavdija Kutnar, Dragan Marušič, Primož Šparl, Ru-Ji Wang, Ming-Yao Xu, 2013, izvirni znanstveni članek

Najdeno v: osebi
Ključne besede: graph
Objavljeno: 15.10.2013; Ogledov: 1143; Prenosov: 10
URL Polno besedilo (0,00 KB)

29.
Classification of edge-transitive rose window graphs
István Kovács, Klavdija Kutnar, Dragan Marušič, 2010, izvirni znanstveni članek

Opis: Given natural numbers ▫$n \ge 3$▫ and ▫$1 \le a$▫, ▫$r \le n-1$▫, the rose window graph ▫$R_n(a,r)$▫ is a quartic graph with vertex set ▫$\{x_i \vert i \in {\mathbb Z}_n\} \cup \{y_i \vert i \in {\mathbb Z}_n\}$▫ and edge set ▫$\{\{x_i, x_{i+1}\} \vert i \in {\mathbb Z}_n\} \cup \{\{y_i, y_{i+r}\} \vert i \in {\mathbb Z}_n\} \cup \{\{x_i, y_i\} \vert i \in {\mathbb Z}_n\} \cup \{\{x_{i+a}, y_i\} \vert i \in {\mathbb Z}_n\}$▫. In this article a complete classification of edge-transitive rose window graphs is given, thus solving one of three open problems about these graphs posed by Steve Wilson in 2001.
Najdeno v: osebi
Ključne besede: group, graph, rose window, vertex-transitive, edge-transitive, arc-transitive
Objavljeno: 15.10.2013; Ogledov: 1281; Prenosov: 45
URL Polno besedilo (0,00 KB)

30.
On cubic non-Cayley vertex-transitive graphs
Klavdija Kutnar, Dragan Marušič, Cui Zhang, 2012, izvirni znanstveni članek

Najdeno v: osebi
Ključne besede: vertex-transitive graph, non-Cayley graph, automorphism group
Objavljeno: 15.10.2013; Ogledov: 1203; Prenosov: 57
URL Polno besedilo (0,00 KB)

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