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The Automorphism Groups of Small Affine Rank 3 Graphs Full article

Journal Communications in Mathematics and Statistics
ISSN: 2194-6701 , E-ISSN: 2194-671X
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 Guo Jin 1 , Vasil'ev Andrey V. 2 , Wang Rui 1
Affiliations
1 School of Mathematics and Statistics, Hainan University, Haikou, 570228, Hainan, People's Republic of China
2 Sobolev Institute of Mathematics, Novosibirsk, 630090, Russia

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
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
Citing:
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Web of science 1
OpenAlex 1
Scopus 1
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