A census of Cayley graphs
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866914181847973888 |
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| author | Evans, Rhys J. Potočnik, Primož |
| author_facet | Evans, Rhys J. Potočnik, Primož |
| contents | Given positive integers $k$ and $n$, we present methods to construct all groups of order at most $n$ that contain a Cayley set of size $k$, and to enumerate the Cayley sets of order $k$ in a given group, up to the action of the automorphism group. We use these methods to generate complete lists of pairwise nonisomorphic 3-valent Cayley graphs with at most 5000 vertices and 4-valent Cayley graphs with at most 1025 vertices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_05406 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A census of Cayley graphs Evans, Rhys J. Potočnik, Primož Combinatorics Group Theory Given positive integers $k$ and $n$, we present methods to construct all groups of order at most $n$ that contain a Cayley set of size $k$, and to enumerate the Cayley sets of order $k$ in a given group, up to the action of the automorphism group. We use these methods to generate complete lists of pairwise nonisomorphic 3-valent Cayley graphs with at most 5000 vertices and 4-valent Cayley graphs with at most 1025 vertices. |
| title | A census of Cayley graphs |
| topic | Combinatorics Group Theory |
| url | https://arxiv.org/abs/2512.05406 |