Enregistré dans:
| Auteurs principaux: | , , , , , |
|---|---|
| Format: | Preprint |
| Publié: |
2023
|
| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2302.00994 |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866913599324160000 |
|---|---|
| author | Berman, Leah Wrenn Koike, Hiroki Mochan, Elias Ramos-Rivera, Alejandra Sparl, Primoz Wilson, Stephen E. |
| author_facet | Berman, Leah Wrenn Koike, Hiroki Mochan, Elias Ramos-Rivera, Alejandra Sparl, Primoz Wilson, Stephen E. |
| contents | A graph is edge-transitive if the natural action of its automorphism group on its edge set is transitive. An automorphism of a graph is semiregular if all of the orbits of the subgroup generated by this automorphism have the same length. While the tetravalent edge-transitive graphs admitting a semiregular automorphism with only one orbit are easy to determine, those that admit a semiregular automorphism with two orbits took a considerable effort and were finally classified in 2012. Of the several possible different ``types'' of potential tetravalent edge-transitive graphs admitting a semiregular automorphism with three orbits, only one ``type'' has thus far received no attention. In this paper we focus on this class of graphs, which we call the Woolly Hat graphs. We prove that there are in fact no edge-transitive Woolly Hat graphs and classify the vertex-transitive ones. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_00994 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Symmetries of the Woolly Hat graphs Berman, Leah Wrenn Koike, Hiroki Mochan, Elias Ramos-Rivera, Alejandra Sparl, Primoz Wilson, Stephen E. Combinatorics 05C25 A graph is edge-transitive if the natural action of its automorphism group on its edge set is transitive. An automorphism of a graph is semiregular if all of the orbits of the subgroup generated by this automorphism have the same length. While the tetravalent edge-transitive graphs admitting a semiregular automorphism with only one orbit are easy to determine, those that admit a semiregular automorphism with two orbits took a considerable effort and were finally classified in 2012. Of the several possible different ``types'' of potential tetravalent edge-transitive graphs admitting a semiregular automorphism with three orbits, only one ``type'' has thus far received no attention. In this paper we focus on this class of graphs, which we call the Woolly Hat graphs. We prove that there are in fact no edge-transitive Woolly Hat graphs and classify the vertex-transitive ones. |
| title | Symmetries of the Woolly Hat graphs |
| topic | Combinatorics 05C25 |
| url | https://arxiv.org/abs/2302.00994 |