1. Hamilton paths in vertextransitive graphs of order 10pDragan Marušič, Klavdija Kutnar, Cui Zhang, 2012, original scientific article Abstract: It is shown that every connected vertextransitive 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 ▫$\mathbb{Z}_k \times \mathbb{Z}_{(k1)/10}$▫, contains a Hamilton path. Found in: osebi Keywords: graph, vertextransitive, Hamilton cycle, Hamilton path, automorphism group Published: 15.10.2013; Views: 2965; Downloads: 36 Full text (0,00 KB) 
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4. On quartic halfarctransitive metacirculantsDragan Marušič, Primož Šparl, 2008, original scientific article Abstract: Following Alspach and Parsons, a metacirculant graph is a graph admitting a transitive group generated by two automorphisms ▫$\rho$▫ and ▫$\sigma$▫, where ▫$\rho$▫ is ▫$(m,n)$▫semiregular for some integers ▫$m \ge 1$▫, ▫$n \ge 2▫$, and where ▫$\sigma$▫ normalizes ▫$\rho$▫, cyclically permuting the orbits of ▫$\rho$▫ in such a way that ▫$\sigma^m$▫ has at least one fixed vertex. A halfarctransitive graph is a vertex and edge but not arctransitive graph. In this article quartic halfarctransitive metacirculants are explored and their connection to the so called tightly attached quartic halfarctransitive graphs is explored. It is shown that there are three essentially different possibilities for a quartic halfarctransitive metacirculant which is not tightly attached to exist. These graphs are extensively studied and some infinite families of such graphs are constructed. Found in: osebi Keywords: mathematics, graph theory, metacirculant graph, halfarctransitive graph, tightly attached, automorphism group Published: 15.10.2013; Views: 3036; Downloads: 125 Full text (0,00 KB) 
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8. The strongly distancebalanced property of the generalized Petersen graphsŠtefko Miklavič, Dragan Marušič, Aleksander Malnič, Klavdija Kutnar, 2009, original scientific article Abstract: A graph ▫$X$▫ is said to be strongly distancebalanced whenever for any edge ▫$uv$▫ of ▫$X$▫ and any positive integer ▫$i$▫, the number of vertices at distance ▫$i$▫ from ▫$u$▫ and at distance ▫$i + 1$▫ from ▫$v$▫ is equal to the number of vertices at distance ▫$i + 1$▫ from ▫$u$▫ and at distance ▫$i$▫ from ▫$v$▫. It is proven that for any integers ▫$k \ge 2$▫ and ▫$n \ge k^2 + 4k + 1$▫, the generalized Petersen graph GP▫$(n, k)$▫ is not strongly distancebalanced. Found in: osebi Keywords: graph, strongy distancebalanced, generalized Petersen graph Published: 15.10.2013; Views: 2438; Downloads: 126 This document has more files! More...

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