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 1 - 3 / 31 1.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: ključnih besedahSummary of found: ...cubic graphs, symmetric graphs, ▫$s$▫-regular graphs, girth, consistent cycle...Keywords: graph theory, cubic graphs, symmetric graphs, ▫$s$▫-regular graphs, girth, consistent cyclePublished: 15.10.2013; Views: 1827; Downloads: 49 Full text (0,00 KB) 2.Consistent Cycles in 1/2-Arc-Transitive GraphsMarko Boben, Štefko Miklavič, Primož Potočnik, 2009, original scientific articleFound in: ključnih besedahSummary of found: ...mathematics, graph theory, 1/2-arc-transitivity, consistent cycle, ...Keywords: mathematics, graph theory, 1/2-arc-transitivity, consistent cyclePublished: 15.10.2013; Views: 2183; Downloads: 7 Full text (0,00 KB)This document has more files! More... 3.Arc-transitive cycle decompositions of tetravalent graphsŠtefko Miklavič, Primož Potočnik, Stephen Wilson, 2008, original scientific articleAbstract: A cycle decomposition of a graph ▫$\Gamma$▫ is a set ▫$\mathcal{C}$▫ of cycles of ▫$\Gamma$▫ such that every edge of ▫$\Gamma$▫ belongs to exactly one cycle in ▫$\mathcal{C}$▫. Such a decomposition is called arc-transitive if the group of automorphisms of ▫$\Gamma$▫ that preserve setwise acts transitively on the arcs of ▫$\Gamma$▫. In this paper, we study arc-transitive cycle decompositions of tetravalent graphs. In particular, we are interested in determining and enumerating arc-transitive cycle decompositions admitted by a given arc-transitive tetravalent graph. Among other results we show that a connected tetravalent arc-transitive graph is either 2-arc-transitive, or is isomorphic to the medial graph of a reflexible map, or admits exactly one cycle structure.Found in: ključnih besedahSummary of found: ...mathematics, graph theory, cycle decomposition, automorphism group, consistent cycle, medial maps...Keywords: mathematics, graph theory, cycle decomposition, automorphism group, consistent cycle, medial mapsPublished: 15.10.2013; Views: 1418; Downloads: 48 Full text (0,00 KB)
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