Geodesic
Classification of $(v,5)$-configurations for $v \leq 11$
Diskretnaya Matematika, Tome 36 (2024) no. 1, pp. 46-66 Cet article a éte moissonné depuis la source Math-Net.Ru

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The combinatorial objects — $(v,k)$-configurations are studied for $k=5$. A theorem on necessary and sufficient conditions of combinatorial equivalence of $(v,5)$-configurations constructed by digraphs with two input and two output arcs at each vertex is proved. Algorithms for constructing $(v,5)$-configurations and identifying combinatorially equivalent ones among them are developed. An exhaustive classification of $(v,5)$-configurations for $v\leq11$ is obtained. Discribing of $(v,5)$-configurations for $v\leqslant 10$ is given and the number of combinatorially non-equivalent $(11,5)$-configurations is pointed.
Mots-clés : $(v,k)$-configurations, $(v,k)$-matrices
Keywords: digraphs, finite groups. 
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M. M. Komiagin. Classification of $(v,5)$-configurations for $v \leq 11$. Diskretnaya Matematika, Tome 36 (2024) no. 1, pp. 46-66. http://geodesic.mathdoc.fr/item/DM_2024_36_1_a2/

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