Cubic vertex-transitive graphs of girth six
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2020
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| _version_ | 1866916548615077888 |
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| author | Potočnik, Primož Vidali, Janoš |
| author_facet | Potočnik, Primož Vidali, Janoš |
| contents | In this paper, a complete classification of finite simple cubic vertex-transitive graphs of girth $6$ is obtained. It is proved that every such graph, with the exception of the Desargues graph on $20$ vertices, is either a skeleton of a hexagonal tiling of the torus, the skeleton of the truncation of an arc-transitive triangulation of a closed hyperbolic surface, or the truncation of a $6$-regular graph with respect to an arc-transitive dihedral scheme. Cubic vertex-transitive graphs of girth larger than $6$ are also discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2005_01635 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Cubic vertex-transitive graphs of girth six Potočnik, Primož Vidali, Janoš Combinatorics 20B25 In this paper, a complete classification of finite simple cubic vertex-transitive graphs of girth $6$ is obtained. It is proved that every such graph, with the exception of the Desargues graph on $20$ vertices, is either a skeleton of a hexagonal tiling of the torus, the skeleton of the truncation of an arc-transitive triangulation of a closed hyperbolic surface, or the truncation of a $6$-regular graph with respect to an arc-transitive dihedral scheme. Cubic vertex-transitive graphs of girth larger than $6$ are also discussed. |
| title | Cubic vertex-transitive graphs of girth six |
| topic | Combinatorics 20B25 |
| url | https://arxiv.org/abs/2005.01635 |