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

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