Parameters of Quotient-Polynomial Graphs
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866916198887718912 |
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| author | Herman, Allen Maleki, Roghayeh |
| author_facet | Herman, Allen Maleki, Roghayeh |
| contents | Fiol has characterized quotient-polynomial graphs as precisely the connected graphs whose adjacency matrix generates the adjacency algebra of a symmetric association scheme. We show that a collection of non-negative integer parameters of size $d + \frac{d(d-1)}{2}$ is adequate for describing symmetric association schemes of class $d$ that are generated by the adjacency matrix of their first non-trivial relation. We use this to generate a database of the corresponding quotient-polynomial graphs that have small valency and up to 6 classes, and among these find new feasible parameter sets for symmetric association schemes with noncyclotomic eigenvalues. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2309_03657 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Parameters of Quotient-Polynomial Graphs Herman, Allen Maleki, Roghayeh Combinatorics Primary 05E30, Secondary 05E16, 05C75, 13P99, 42C05 Fiol has characterized quotient-polynomial graphs as precisely the connected graphs whose adjacency matrix generates the adjacency algebra of a symmetric association scheme. We show that a collection of non-negative integer parameters of size $d + \frac{d(d-1)}{2}$ is adequate for describing symmetric association schemes of class $d$ that are generated by the adjacency matrix of their first non-trivial relation. We use this to generate a database of the corresponding quotient-polynomial graphs that have small valency and up to 6 classes, and among these find new feasible parameter sets for symmetric association schemes with noncyclotomic eigenvalues. |
| title | Parameters of Quotient-Polynomial Graphs |
| topic | Combinatorics Primary 05E30, Secondary 05E16, 05C75, 13P99, 42C05 |
| url | https://arxiv.org/abs/2309.03657 |