Finite skew braces with isomorphic non-abelian characteristically simple additive and circle groups

A skew brace is a triplet (A, center dot, omicron), where (A, center dot) and (A, omicron) are groups such that the brace relation x omicron (y center dot z) = (x omicron y) center dot x(-1) center dot (x omicron z) holds for all x, y, z is an element of A. In this paper, we study the number of finite skew braces (A, center dot, omicron), up to isomorphism, such that (A, center dot) and (A, omicron) are both isomorphic to T-n with T non-abelian simple and n is an element of N. We prove that it is equal to the number of unlabeled directed graphs on n + 1 vertices, with one distinguished vertex, and whose underlying undirected graph is a tree. In particular, it depends only on n and is independent of T.