Symmetries of the Honeycomb toroidal graphs
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arXiv
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| Format: | Preprint |
| Published: |
2020
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| _version_ | 1866916509449715712 |
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| author | Sparl, Primoz |
| author_facet | Sparl, Primoz |
| contents | {\em Honeycomb toroidal graphs} are a family of cubic graphs determined by a set of three parameters, that have been studied over the last three decades both by mathematicians and computer scientists. They can all be embedded on a torus and coincide with the cubic Cayley graphs of generalized dihedral groups with respect to a set of three reflections. In a recent survey paper B. Alspach gathered most known results on this intriguing family of graphs and suggested a number of research problems regarding them. In this paper we solve two of these problems by determining the full automorphism group of each honeycomb toroidal graph. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2011_14609 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Symmetries of the Honeycomb toroidal graphs Sparl, Primoz Combinatorics 05C25, 20B25 {\em Honeycomb toroidal graphs} are a family of cubic graphs determined by a set of three parameters, that have been studied over the last three decades both by mathematicians and computer scientists. They can all be embedded on a torus and coincide with the cubic Cayley graphs of generalized dihedral groups with respect to a set of three reflections. In a recent survey paper B. Alspach gathered most known results on this intriguing family of graphs and suggested a number of research problems regarding them. In this paper we solve two of these problems by determining the full automorphism group of each honeycomb toroidal graph. |
| title | Symmetries of the Honeycomb toroidal graphs |
| topic | Combinatorics 05C25, 20B25 |
| url | https://arxiv.org/abs/2011.14609 |