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 university Found in: ključnih besedah Summary of found: ...automorphism group, ... Keywords: automorphism group Published: 15.10.2013; Views: 1677; Downloads: 11 Full text (0,00 KB) |
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3. Hamilton paths in vertex-transitive graphs of order 10pKlavdija 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. Found in: ključnih besedah Summary of found: ...graph, vertex-transitive, Hamilton cycle, Hamilton path, automorphism group... Keywords: graph, vertex-transitive, Hamilton cycle, Hamilton path, automorphism group Published: 15.10.2013; Views: 1774; Downloads: 12 Full text (0,00 KB) |
4. Hamiltonicity of vertex-transitive graphs of order 4pKlavdija 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. Found in: ključnih besedah Summary of found: ...graph theory, vertex-transitive graphs, Hamilton cycle, automorphism group... Keywords: graph theory, vertex-transitive graphs, Hamilton cycle, automorphism group Published: 15.10.2013; Views: 1650; Downloads: 18 Full text (0,00 KB) |
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7. 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: ključnih besedah Summary of found: ...theory, metacirculant graph, half-arc-transitive graph, tightly attached, automorphism group... Keywords: mathematics, graph theory, metacirculant graph, half-arc-transitive graph, tightly attached, automorphism group Published: 15.10.2013; Views: 1733; Downloads: 68 Full text (0,00 KB) |
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9. Asymptotic automorphism groups of Cayley digraphs and graphs of abelian groups of prime-power orderEdward Dobson, 2010, original scientific article Abstract: We show that almost every Cayley graph ▫$\Gamma$▫ of an abelian group ▫$G$▫ of odd prime-power order has automorphism group as small as possible. Additionally, we show that almost every Cayley (di)graph ▫$\Gamma$▫ of an abelian group ▫$G$▫ of odd prime-power order that does not have automorphism group as small as possible is a normal Cayley (di)graph of ▫$G$▫ (that is, ▫$G_L \triangleleft {\rm Aut}(\Gamma))$▫. Found in: ključnih besedah Summary of found: ...every Cayley graph ▫$\Gamma$▫ of an abelian group ▫$G$▫ of odd prime-power order has automorphism... Keywords: mathematics, graph theory, Cayley graph, abelian group, automorphism group, asymptotic, ▫$p$▫-group Published: 15.10.2013; Views: 2573; Downloads: 62 Full text (0,00 KB) |
10. Hamilton paths and cycles in vertex-transitive graphs of order 6pKlavdija Kutnar, Primož Šparl, 2009, original scientific article Abstract: It is shown that every connected vertex-transitive graph of order ▫$6p$▫, where ▫$p$▫ is a prime, contains a Hamilton path. Moreover, it is shown that, except for the truncation of the Petersen graph, every connected vertex-transitive graph of order ▫$6p$▫ which is not genuinely imprimitive contains a Hamilton cycle. Found in: ključnih besedah Summary of found: ...graph theory, vertex-transitive, Hamilton cycle, Hamilton path, automorphism group... Keywords: graph theory, vertex-transitive, Hamilton cycle, Hamilton path, automorphism group Published: 15.10.2013; Views: 1711; Downloads: 14 Full text (0,00 KB) |