20.500.12556/RUP-1125 A complete classification of cubic symmetric graphs of girth 6 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 ▫$n^2/2$▫. graph theory cubic graphs symmetric graphs ▫$s$▫-regular graphs girth consistent cycle teorija grafov kubični grafi simetrični grafi ▫$s$▫-regularni grafi dolžina najkrajšega cikla true false false Angleški jezik Angleški jezik Delo ni kategorizirano 2013-10-15 12:05:36 2013-10-15 12:05:36 2024-03-01 11:59:57 0000-00-00 00:00:00 2009 0 0 str. 162-184 No. 1 Vol. 99 2009 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 0095-8956 519.17 2724823 http://dx.doi.org/10.1016/j.jctb.2008.06.001 1 https://repozitorij.upr.si/Dokument.php?lang=slv&id=1125 Univerza na Primorskem 0 0 0