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<p>A rank 3 graph is an orbital graph of a rank 3 permutation group of even order. Despite the completion of the classification of rank 3 graphs (see, e.g., Chapter 11 of the recent monograph Strongly regular graphs by Brouwer and Van&#xa0;Maldeghem), the full automorphism groups of these graphs (equivalently, the 2-closures of rank 3 groups) have not been explicitly described, though a lot of information on this subject is available. In the present note, we address this problem for the affine rank 3 graphs. We find the automorphism groups for finitely many relatively small graphs and show that modulo known results, this provides a complete description of the automorphism groups of the affine rank 3 graphs, thus reducing the general problem to the case when the socle of the automorphism group is nonabelian simple.</p>

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The Automorphism Groups of Small Affine Rank 3 Graphs

  • 期刊论文

  • 发表日期：

    2025年11月28日

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  • Jin Guo,
  • Andrey V. Vasil’ev,
  • Rui Wang

摘要

A rank 3 graph is an orbital graph of a rank 3 permutation group of even order. Despite the completion of the classification of rank 3 graphs (see, e.g., Chapter 11 of the recent monograph Strongly regular graphs by Brouwer and Van Maldeghem), the full automorphism groups of these graphs (equivalently, the 2-closures of rank 3 groups) have not been explicitly described, though a lot of information on this subject is available. In the present note, we address this problem for the affine rank 3 graphs. We find the automorphism groups for finitely many relatively small graphs and show that modulo known results, this provides a complete description of the automorphism groups of the affine rank 3 graphs, thus reducing the general problem to the case when the socle of the automorphism group is nonabelian simple.