Classification of $(v,5)$-configurations for $v \leq 11$

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.