1. Hamilton paths in vertex-transitive graphs of order 10pDragan Marušič, Klavdija Kutnar, 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.
Found in: osebi
Keywords: graph, vertex-transitive, Hamilton cycle, Hamilton path, automorphism group
Published: 15.10.2013; Views: 2965; Downloads: 36
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4. On quartic half-arc-transitive 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 half-arc-transitive graph is a vertex- and edge- but not arc-transitive graph. In this article quartic half-arc-transitive metacirculants are explored and their connection to the so called tightly attached quartic half-arc-transitive graphs is explored. It is shown that there are three essentially different possibilities for a quartic half-arc-transitive 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, half-arc-transitive graph, tightly attached, automorphism group
Published: 15.10.2013; Views: 3036; Downloads: 125
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8. The strongly distance-balanced 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 distance-balanced 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 distance-balanced.
Found in: osebi
Keywords: graph, strongy distance-balanced, generalized Petersen graph
Published: 15.10.2013; Views: 2438; Downloads: 126
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