Parameters of Quotient-Polynomial Graphs

Fuente: arXiv
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Main Authors: Herman, Allen, Maleki, Roghayeh
Format: Preprint
Published: 2023
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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
id 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