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71.
Hamiltonicity of vertex-transitive graphs of order 4p
Klavdija Kutnar, Dragan Marušič, 2008, original scientific article

Abstract: 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.
Keywords: graph theory, vertex-transitive graphs, Hamilton cycle, automorphism group
Published in RUP: 15.10.2013; Views: 3539; Downloads: 39
URL Link to full text

72.
Hamilton paths in vertex-transitive graphs of order 10p
Klavdija Kutnar, Dragan Marušič, Cui Zhang, 2012, original scientific article

Abstract: 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.
Keywords: graph, vertex-transitive, Hamilton cycle, Hamilton path, automorphism group
Published in RUP: 15.10.2013; Views: 3487; Downloads: 39
URL Link to full text

73.
An unusual decomposition of a complete 7-partite graph of order 28
Edward Dobson, Dragan Marušič, 2008, original scientific article

Abstract: A decomposition of the complete 7-partite graph on 28 vertices where each set in the partition has four vertices is given. Several unusual properties of this decomposition are discussed, giving rise to several natural questions.
Keywords: matematika, teorija grafov, po točkah tranzitivni grafi, faktorizacija
Published in RUP: 15.10.2013; Views: 3424; Downloads: 84
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74.
On prime-valent symmetric bicirculants and Cayley snarks
Ademir Hujdurović, Klavdija Kutnar, Dragan Marušič, 2013, published scientific conference contribution

Keywords: graph, Cayley graph, arc-transitive, snark, semiregular automorphism, bicirculant
Published in RUP: 15.10.2013; Views: 3322; Downloads: 155
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75.
Classification of cubic symmetric tricirculants
István Kovács, Klavdija Kutnar, Dragan Marušič, Steve Wilson, 2012, original scientific article

Keywords: symmetric graph, semiregular, tricirculant
Published in RUP: 15.10.2013; Views: 3353; Downloads: 82
URL Link to full text

76.
Vertex-transitive expansions of (1, 3)-trees
Marko Lovrečič Saražin, Dragan Marušič, 2010, published scientific conference contribution

Abstract: A nonidentity automorphism of a graph is said to be semiregular if all of its orbits are of the same length. Given a graph ▫$X$▫ with a semiregular automorphism ▫$\gamma$▫, the quotient of ▫$X$▫ relative to ▫$\gamma$▫ is the multigraph ▫$X/\gamma$▫ whose vertices are the orbits of ▫$\gamma$▫ and two vertices are adjacent by an edge with multiplicity ▫$r$▫ if every vertex of one orbit is adjacent to ▫$r$▫ vertices of the other orbit. We say that ▫$X$▫ is an expansion of ▫$X/\gamma$▫. In [J.D. Horton, I.Z. Bouwer, Symmetric ▫$Y$▫-graphs and ▫$H$▫-graphs, J. Combin. Theory Ser. B 53 (1991) 114-129], Hortonand Bouwer considered a restricted sort of expansions (which we will call :strong" in this paper) where every leaf of ▫$X/\gamma$▫ expands to a single cycle in ▫$X$▫. They determined all cubic arc-transitive strong expansions of simple ▫$(1,3)$▫-trees, that is, trees with all of their vertice shaving valency 1 or 3, thus extending the classical result of Frucht, Graver and Watkins (see [R. Frucht, J.E. Graver, M.E. Watkins, The groups of the generalized Petersen graphs, Proc. Cambridge Philos. Soc. 70 (1971) 211-218]) about arc-transitive strong expansions of ▫$K_2$▫ (also known as the generalized Petersen graphs). In this paper another step is taken further by considering the possible structure of cubic vertex-transitive expansions of general ▫$(1,3)$▫-multitrees (where vertices with double edges are also allowed); thus the restriction on every leaf to be expanded to a single cycle is dropped.
Keywords: graph, tree, cubic, vertex-transitive, arc-transitive, expansion
Published in RUP: 15.10.2013; Views: 3960; Downloads: 80
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