The automorphism groups and identification of some Generalized Paley Graphs
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866914168343363584 |
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| author | Ponomarenko, Ilia |
| author_facet | Ponomarenko, Ilia |
| contents | The family of generalized Paley graphs of prime power order $q$ and degree $(q-1)/k$ is studied. It is shown that the automorphism group of a graph in this family is a subgroup of ${\mathrm{AΓL}}(1,q)$ whenever $q$ is sufficiently large relative to $k$. Furthermore, under the same conditions, the Weisfeiler-Leman dimension of these graphs is proved to be at most $5$. In particular, the same bound holds for the Van Lint-Schrijver graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_18304 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The automorphism groups and identification of some Generalized Paley Graphs Ponomarenko, Ilia Combinatorics 05E30, 05E18, 11T99 G.2.1; G.2.2 The family of generalized Paley graphs of prime power order $q$ and degree $(q-1)/k$ is studied. It is shown that the automorphism group of a graph in this family is a subgroup of ${\mathrm{AΓL}}(1,q)$ whenever $q$ is sufficiently large relative to $k$. Furthermore, under the same conditions, the Weisfeiler-Leman dimension of these graphs is proved to be at most $5$. In particular, the same bound holds for the Van Lint-Schrijver graphs. |
| title | The automorphism groups and identification of some Generalized Paley Graphs |
| topic | Combinatorics 05E30, 05E18, 11T99 G.2.1; G.2.2 |
| url | https://arxiv.org/abs/2511.18304 |