Integral Cayley graphs over a finite symmetric algebra

Fuente: arXiv
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Main Authors: Nguyen, Tung T., Tân, Nguyen Duy
Format: Preprint
Published: 2024
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author Nguyen, Tung T.
Tân, Nguyen Duy
author_facet Nguyen, Tung T.
Tân, Nguyen Duy
contents A graph is called integral if its eigenvalues are integers. In this article, we provide the necessary and sufficient conditions for a Cayley graph over a finite symmetric algebra $R$ to be integral. This generalizes the work of So who studies the case where $R$ is the ring of integers modulo $n.$ We also explain some number-theoretic constructions of finite symmetric algebras arising from global fields, which we hope could pave the way for future studies on Paley graphs associated with a finite Hecke character.
format Preprint
id arxiv_https___arxiv_org_abs_2411_00307
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Integral Cayley graphs over a finite symmetric algebra
Nguyen, Tung T.
Tân, Nguyen Duy
Number Theory
Combinatorics
11R58, 05E40, 05C50
A graph is called integral if its eigenvalues are integers. In this article, we provide the necessary and sufficient conditions for a Cayley graph over a finite symmetric algebra $R$ to be integral. This generalizes the work of So who studies the case where $R$ is the ring of integers modulo $n.$ We also explain some number-theoretic constructions of finite symmetric algebras arising from global fields, which we hope could pave the way for future studies on Paley graphs associated with a finite Hecke character.
title Integral Cayley graphs over a finite symmetric algebra
topic Number Theory
Combinatorics
11R58, 05E40, 05C50
url https://arxiv.org/abs/2411.00307