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<p>A graph is called integral if its eigenvalues are integers. In this article, we provide necessary and sufficient conditions for a Cayley graph over a finite symmetric algebra <i>R</i> to be integral. This generalizes the work of So who studies the case where <i>R</i> is the ring of integers modulo <i>n</i>. 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 finite Hecke characters.</p>

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Integral Cayley graphs over a finite symmetric algebra

  • 期刊论文

  • 发表日期：

    2025年3月11日

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  • Tung T. Nguyen,
  • Nguyễn Duy Tân

摘要

A graph is called integral if its eigenvalues are integers. In this article, we provide 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 finite Hecke characters.