Neumaier graphs from cyclotomy with small coherent rank
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866912331261280256 |
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| author | Greaves, Gary R. W. Tan, Zhao Kuang |
| author_facet | Greaves, Gary R. W. Tan, Zhao Kuang |
| contents | Using cyclotomy, we construct a new infinite family of Neumaier graphs that includes infinitely many strongly regular graphs. Notably, this family conjecturally contains infinitely many graphs with coherent rank $6$. Our construction also provides the first known examples that answer a question posed by Evans, Goryainov, and Panasenko regarding the existence of Neumaier graphs whose nexus is not a power of $2$. In addition, we show that a construction of Greaves and Koolen yields an infinite family of Neumaier graphs with coherent rank $6$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_12026 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Neumaier graphs from cyclotomy with small coherent rank Greaves, Gary R. W. Tan, Zhao Kuang Combinatorics Using cyclotomy, we construct a new infinite family of Neumaier graphs that includes infinitely many strongly regular graphs. Notably, this family conjecturally contains infinitely many graphs with coherent rank $6$. Our construction also provides the first known examples that answer a question posed by Evans, Goryainov, and Panasenko regarding the existence of Neumaier graphs whose nexus is not a power of $2$. In addition, we show that a construction of Greaves and Koolen yields an infinite family of Neumaier graphs with coherent rank $6$. |
| title | Neumaier graphs from cyclotomy with small coherent rank |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2504.12026 |