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European project for truancy prevention and mental health promotion - WE STAY project
Marianna D'Aulerio, Dragan Marušič, Vita Poštuvan, 2012, published scientific conference contribution abstract

Found in: osebi
Keywords: WE-STAY, truancy, adolescents, mental health promotion, preventive programme
Published: 15.10.2013; Views: 1922; Downloads: 14
URL Full text (0,00 KB)

Hamiltonicity of cubic Cayley graphs
Dragan Marušič, Henry Glover, Klavdija Kutnar, Aleksander Malnič, 2012, published scientific conference contribution abstract (invited lecture)

Found in: osebi
Keywords: Cayley graph, Hamilton path, Hamilton cycle, arc-transitive graph, Cayley map
Published: 15.10.2013; Views: 1402; Downloads: 29
URL Full text (0,00 KB)

On 2-fold covers of graphs
Yan-Quan Feng, Klavdija Kutnar, Aleksander Malnič, Dragan Marušič, 2008, original scientific article

Abstract: 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.
Found in: osebi
Keywords: graph theory, graphs, cubic graphs, symmetric graphs, ▫$s$▫-regular group, regular covering projection
Published: 15.10.2013; Views: 1293; Downloads: 14
URL Full text (0,00 KB)

Recent trends and future directions in vertex-transitive graphs
Klavdija Kutnar, Dragan Marušič, 2008, original scientific article

Abstract: 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.
Found in: osebi
Keywords: matematika, teorija grafov, tranzitivni grafi, poltranzitivni grafi, Hamiltonov cikel, delovanje grupe, polregularna grupa
Published: 15.10.2013; Views: 1538; Downloads: 60
URL Full text (0,00 KB)

Fullerenes via their automorphism groups
Klavdija Kutnar, Dragan Marušič, Dušanka Janežič, 2010, original scientific article

Found in: osebi
Keywords: matematika, morfologija, avtomorfizem, fulereni
Published: 15.10.2013; Views: 1699; Downloads: 13
URL Full text (0,00 KB)

Classification of half-arc-transitive graphs of order 4p
Klavdija Kutnar, Dragan Marušič, Primož Šparl, Ru-Ji Wang, Ming-Yao Xu, 2013, original scientific article

Found in: osebi
Keywords: graph
Published: 15.10.2013; Views: 1183; Downloads: 10
URL Full text (0,00 KB)

Classification of edge-transitive rose window graphs
István Kovács, Klavdija Kutnar, Dragan Marušič, 2010, original scientific article

Abstract: 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.
Found in: osebi
Keywords: group, graph, rose window, vertex-transitive, edge-transitive, arc-transitive
Published: 15.10.2013; Views: 1330; Downloads: 51
URL Full text (0,00 KB)

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

Found in: osebi
Keywords: vertex-transitive graph, non-Cayley graph, automorphism group
Published: 15.10.2013; Views: 1273; Downloads: 63
URL Full text (0,00 KB)

An introduction to graph theory
Dragan Marušič, 2006, other educational material

Found in: osebi
Keywords: graph theory
Published: 15.10.2013; Views: 1611; Downloads: 54
URL Full text (0,00 KB)

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