| Title: | A complete classification of cubic symmetric graphs of girth 6 |
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| Authors: | ID Kutnar, Klavdija (Author)
ID Marušič, Dragan (Author) |
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| Files: |  http://dx.doi.org/10.1016/j.jctb.2008.06.001
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| Language: | English |
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| Work type: | Not categorized |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: | UPR - University of Primorska
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| 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 ▫$n^2/2$▫. |
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| Keywords: | graph theory, cubic graphs, symmetric graphs, ▫$s$▫-regular graphs, girth, consistent cycle |
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| Year of publishing: | 2009 |
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| Number of pages: | str. 162-184 |
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| Numbering: | Vol. 99, No. 1 |
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| PID: | 20.500.12556/RUP-1125  |
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| ISSN: | 0095-8956 |
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| UDC: | 519.17 |
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| COBISS.SI-ID: | 2724823 |
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| Publication date in RUP: | 15.10.2013 |
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| Views: | 4538 |
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| Downloads: | 87 |
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