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