Second largest maximal cliques in small Paley graphs of square order
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866912060242132992 |
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| author | Chen, Huye Goryainov, Sergey Hu, Cong |
| author_facet | Chen, Huye Goryainov, Sergey Hu, Cong |
| contents | There is a conjecture that the second largest maximal cliques in Paley graphs of square order $P(q^2)$ have size $\frac{q+ε}{2}$, where $q \equiv ε\pmod 4$, and split into two orbits under the full group of automorphisms whenever $q \ge 25$ (a symmetric description for these two orbits is known). However, some extra second largest maximal cliques (of this size) exist in $P(q^2)$ whenever $q \in \{9,11,13,17,19,23\}$. In this paper we analyse the algebraic and geometric structure of the extra cliques. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_04024 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Second largest maximal cliques in small Paley graphs of square order Chen, Huye Goryainov, Sergey Hu, Cong Combinatorics There is a conjecture that the second largest maximal cliques in Paley graphs of square order $P(q^2)$ have size $\frac{q+ε}{2}$, where $q \equiv ε\pmod 4$, and split into two orbits under the full group of automorphisms whenever $q \ge 25$ (a symmetric description for these two orbits is known). However, some extra second largest maximal cliques (of this size) exist in $P(q^2)$ whenever $q \in \{9,11,13,17,19,23\}$. In this paper we analyse the algebraic and geometric structure of the extra cliques. |
| title | Second largest maximal cliques in small Paley graphs of square order |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2410.04024 |