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arXiv · 2309.03657

Parameters of Quotient-Polynomial Graphs

Allen Herman·Roghayeh Maleki
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Abstract

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.

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Allen Herman, Roghayeh Maleki. 2024-04-09. Parameters of Quotient-Polynomial Graphs. https://arxiv.org/abs/2309.03657

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