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Diskretnaya Matematika, 2025, Volume 37, Issue 1, Pages 22–38
DOI: https://doi.org/10.4213/dm1830
(Mi dm1830)
 

Classification and properties (12,5)-configurations

M. M. Komiagin

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Abstract: The combinatorial objects — (v,k)-configurations are studied for k=5. All (12,5)-configurations constructed by 2-orgraphs with 6 vertices and by groups of order 12 are described. The number of combinatorially non-equivalent (12,5)-configurations is computed, new examples of (12,5)-configurations are provided. Some properties of (12,5)-configurations are studied: a set of vertex types and a group of automorphisms. An algorithm for constructing an automorphism group of an arbitrary (v,5)-configuration is developed. A theorem on the structure of the automorphism group for (v,5) configurations from some series is proved.
Keywords: (v,k)-configurations, (v,k)-matrices, orgraphs, group of automorphisms.
Received: 17.06.2024
Document Type: Article
UDC: 519.14
Language: Russian
Citation: M. M. Komiagin, “Classification and properties (12,5)-configurations”, Diskr. Mat., 37:1 (2025), 22–38
Citation in format AMSBIB
\Bibitem{Kom25}
\by M.~M.~Komiagin
\paper Classification and properties (12,5)-configurations
\jour Diskr. Mat.
\yr 2025
\vol 37
\issue 1
\pages 22--38
\mathnet{http://mi.mathnet.ru/dm1830}
\crossref{https://doi.org/10.4213/dm1830}
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