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<p>We study cliques in graphs arising from quadratic forms where the vertices are the elements of the module of the quadratic form and two vertices are adjacent if their difference represents some fixed scalar. We determine structural properties and the clique number for quadratic forms over finite rings. We further extend previous results about graphs arising from such forms and forms over fields of characteristic 0 in a unified framework.</p>

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Cliques in representation graphs of quadratic forms

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年1月6日

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  • Nico Lorenz,
  • Marc Christian Zimmermann

摘要

We study cliques in graphs arising from quadratic forms where the vertices are the elements of the module of the quadratic form and two vertices are adjacent if their difference represents some fixed scalar. We determine structural properties and the clique number for quadratic forms over finite rings. We further extend previous results about graphs arising from such forms and forms over fields of characteristic 0 in a unified framework.