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 1 - 10 / 7712345678 1.Graphs and their automorphism groups bpredavanje eUnidad Cuernavaca del Instituto de Matemáticas, UNAM, Cuernavaca, Morelos, Mehika, 23. - 27. 7. 2012Klavdija Kutnar, Primož Šparl, 2012, invited lecture at foreign universityFound in: osebiKeywords: automorphism groupPublished: 15.10.2013; Views: 1593; Downloads: 11 Full text (0,00 KB) 2.Classification of cubic symmetric tricirculantsIstván Kovács, Klavdija Kutnar, Dragan Marušič, Stephen Wilson, 2012, original scientific articleFound in: osebiKeywords: symmetric graph, semiregular, tricirculantPublished: 15.10.2013; Views: 1549; Downloads: 19 Full text (0,00 KB) 3.Hamilton paths in vertex-transitive graphs of order 10pKlavdija Kutnar, Dragan Marušič, Cui Zhang, 2012, original scientific articleAbstract: 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.Found in: osebiKeywords: graph, vertex-transitive, Hamilton cycle, Hamilton path, automorphism groupPublished: 15.10.2013; Views: 1688; Downloads: 11 Full text (0,00 KB) 4.On prime-valent symmetric bicirculants and Cayley snarksAdemir Hujdurović, Klavdija Kutnar, Dragan Marušič, 2013, published scientific conference contributionFound in: osebiKeywords: graph, Cayley graph, arc-transitive, snark, semiregular automorphism, bicirculantPublished: 15.10.2013; Views: 1557; Downloads: 73 Full text (0,00 KB) 5.Hamilton cycles and paths in vertex-transitive graphsKlavdija Kutnar, 2011, invited lecture at foreign universityFound in: osebiKeywords: Hamilton cyclesPublished: 15.10.2013; Views: 1105; Downloads: 18 Full text (0,00 KB) 6.Hamiltonicity of vertex-transitive graphs of order 4pKlavdija Kutnar, Dragan Marušič, 2008, original scientific articleAbstract: 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.Found in: osebiKeywords: graph theory, vertex-transitive graphs, Hamilton cycle, automorphism groupPublished: 15.10.2013; Views: 1566; Downloads: 17 Full text (0,00 KB) 7.Edge-transitive Rose Window graphsKlavdija Kutnar, 2008, invited lecture at foreign universityFound in: osebiPublished: 15.10.2013; Views: 2236; Downloads: 20 Full text (0,00 KB) 8.Distance-balanced graphs: Symmetry conditionsKlavdija Kutnar, Aleksander Malnič, Dragan Marušič, Štefko Miklavič, 2006, original scientific articleAbstract: A graph ▫$X$▫ is said to be distance-balanced if for any edge ▫$uv$▫ of ▫$X$▫, the number of vertices closer to ▫$u$▫ than to ▫$v$▫ is equal to the number of vertices closer to ▫$v$▫ than to ▫$u$▫. A graph ▫$X$▫ is said to be strongly distance-balanced if for any edge ▫$uv$▫ of ▫$X$▫ and any integer ▫$k$▫, the number of vertices at distance ▫$k$▫ from ▫$u$▫ and at distance ▫$k+1$▫ from ▫$v$▫ is equal to the number of vertices at distance ▫$k+1$▫ from ▫$u$▫ and at distance ▫$k$▫ from ▫$v$▫. Exploring the connection between symmetry properties of graphs and the metric property of being (strongly) distance-balanced is the main theme of this article. That a vertex-transitive graph is necessarily strongly distance-balanced and thus also distance-balanced is an easy observation. With only a slight relaxation of the transitivity condition, the situation changes drastically: there are infinite families of semisymmetric graphs (that is, graphs which are edge-transitive, but not vertex-transitive) which are distance-balanced, but there are also infinite families of semisymmetric graphs which are not distance-balanced. Results on the distance-balanced property in product graphs prove helpful in obtaining these constructions. Finally, a complete classification of strongly distance-balanced graphs is given for the following infinite families of generalized Petersen graphs: GP▫$(n,2)$▫, GP▫$(5k+1,k)$▫, GP▫$(3k 3,k)$▫, and GP▫$(2k+2,k)$▫.Found in: osebiKeywords: graph theory, graph, distance-balanced graphs, vertex-transitive, semysimmetric, generalized Petersen graphPublished: 15.10.2013; Views: 1811; Downloads: 45 Full text (0,00 KB) 9.Hamilton cycles and paths in vertex-transitive graphsKlavdija Kutnar, 2008, invited lecture at foreign universityFound in: osebiPublished: 15.10.2013; Views: 2081; Downloads: 9 Full text (0,00 KB) 10.A complete classification of cubic symmetric graphs of girth 6Klavdija Kutnar, Dragan Marušič, 2009, original scientific articleAbstract: A complete classification of cubic symmetric graphs of girth 6 is given. It is shown that with the exception of the Heawood graph, the Moebius-Kantor graph, the Pappus graph, and the Desargues graph, a cubic symmetric graph ▫$X$▫ of girth 6 is a normal Cayley graph of a generalized dihedral group; in particular, (i) ▫$X$▫ is 2-regular if and only if it is isomorphic to a so-called ▫$I_k^n$▫-path, a graph of order either ▫$n^2/2$▫ or ▫$n^2/6$▫, which is characterized by the fact that its quotient relative to a certain semiregular automorphism is a path. (ii) ▫$X$▫ is 1-regular if and only if there exists an integer ▫$r$▫ with prime decomposition ▫$r=3^s p_1^{e_1} \dots p_t^{e_t} > 3$▫, where ▫$s \in \{0,1\}$▫, ▫$t \ge 1$▫, and ▫$p_i \equiv 1 \pmod{3}$▫, such that ▫$X$▫ is isomorphic either to a Cayley graph of a dihedral group ▫$D_{2r}$▫ of order ▫$2r$▫ or ▫$X$▫ is isomorphic to a certain ▫$\ZZ_r$▫-cover of one of the following graphs: the cube ▫$Q_3$▫, the Pappus graph or an ▫$I_k^n(t)$▫-path of order ▫$n^2/2$▫.Found in: osebiKeywords: graph theory, cubic graphs, symmetric graphs, ▫$s$▫-regular graphs, girth, consistent cyclePublished: 15.10.2013; Views: 1782; Downloads: 44 Full text (0,00 KB)
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