The Automorphism Groups of Small Affine Rank 3 Graphs Full article
| Journal |
Communications in Mathematics and Statistics
ISSN: 2194-6701 , E-ISSN: 2194-671X |
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| Output data | Year: 2025, Pages: 1-16 Pages count : 16 DOI: 10.1007/s40304-025-00456-3 | ||||
| Tags | Affine permutation group · Closure of permutation group · Orbital graph · Full automorphism group of graph · Rank 3 group · Rank 3 graph | ||||
| Authors |
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| Affiliations |
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Funding (1)
| 1 | Sobolev Institute of Mathematics | FWNF-2022-0002 |
Abstract:
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.
Cite:
Guo J.
, Vasil'ev A.V.
, Wang R.
The Automorphism Groups of Small Affine Rank 3 Graphs
Communications in Mathematics and Statistics. 2025. P.1-16. DOI: 10.1007/s40304-025-00456-3 WOS Scopus РИНЦ OpenAlex
The Automorphism Groups of Small Affine Rank 3 Graphs
Communications in Mathematics and Statistics. 2025. P.1-16. DOI: 10.1007/s40304-025-00456-3 WOS Scopus РИНЦ OpenAlex
Dates:
| Submitted: | Feb 24, 2025 |
| Accepted: | May 13, 2025 |
| Published online: | Nov 28, 2025 |
Identifiers:
| Web of science: | WOS:001626279600001 |
| Scopus: | 2-s2.0-105023531303 |
| Elibrary: | 87410718 |
| OpenAlex: | W4416777761 |