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arXiv · 2406.04559

The automorphism groups of small affine rank 3 graphs

Jin Guo·Andrey V. Vasil'ev·Rui Wang
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Abstract

A rank 3 graph is an orbital graph of a rank 3 permutation group of even order. Despite the classification of rank 3 graphs being complete, 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 the full 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.

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Jin Guo, Andrey V. Vasil'ev, Rui Wang. 2024-06-07. The automorphism groups of small affine rank 3 graphs. https://arxiv.org/abs/2406.04559

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