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Title:A complete classification of cubic symmetric graphs of girth 6
Authors:Kutnar, Klavdija (Author)
Marušič, Dragan (Author)
Work type:Not categorized
Tipology:1.01 - Original Scientific Article
Organization:FHŠ - Faculty of Humanities
Abstract: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 ▫$n^2/2$▫.
Keywords:graph theory, cubic graphs, symmetric graphs, ▫$s$▫-regular graphs, girth, consistent cycle
Year of publishing:2009
Number of pages:str. 162-184
Numbering:Vol. 99, No. 1
COBISS_ID:2724823 Link is opened in a new window
Categories:Document is not linked to any category.
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Keywords:teorija grafov, kubični grafi, simetrični grafi, ▫$s$▫-regularni grafi, dolžina najkrajšega cikla


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