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<p>A <i>nut graph</i> is a simple graph of order 2 or more for which the adjacency matrix has a single zero eigenvalue such that all nonzero kernel eigenvectors have no zero entry (i.e. are full). It is shown by construction that every finite group can be represented as the group of automorphisms of infinitely many nut graphs. It is further shown that such nut graphs exist even within the class of regular graphs; the cases where the degree is 8,&#xa0;12,&#xa0;16,&#xa0;20 or 24 are realised explicitly.</p>

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Nut graphs with a given automorphism group

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年2月18日

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  • Nino Bašić,
  • Patrick W. Fowler

摘要

A nut graph is a simple graph of order 2 or more for which the adjacency matrix has a single zero eigenvalue such that all nonzero kernel eigenvectors have no zero entry (i.e. are full). It is shown by construction that every finite group can be represented as the group of automorphisms of infinitely many nut graphs. It is further shown that such nut graphs exist even within the class of regular graphs; the cases where the degree is 8, 12, 16, 20 or 24 are realised explicitly.