strongly semiconnected graphs.

We call a graph $G \in \Gamma_{n,k}$ [*acyclic*]{} if it contains no directed cycles. Recall that a vertex $a$ of the graph $G$ is called a [*sink*]{} if $G$ has no edges starting from $a$. Note that an isolated vertex is a sink but a vertex with a loop attached to it is not. We denote by $\AC_{n,k}^{\{i_1 {, \dots ,} i_s\}}$ the set of acyclic graphs $G \in
\Gamma_{n,k}$ such that the vertices $i_1 {, \dots ,} i_s$, and only they, are sinks. By $\AC_{n,k} {\stackrel{\mbox{\scriptsize def}}{=}}\bigcup_{I \subset \{1 {, \dots ,} n\}} \AC_{n,k}^I$ we will denote the set of all acyclic graphs.

\[Ex:SSC\] If a vertex of a strongly semiconnected graph $G \in \SSC_{n,k}^I$ is not isolated then there is at least one edge starting from it; so if $I = \{i_1
{, \dots ,} i_s\}$ and $\SSC_{n,k}^I \ne {\varnothing}$ then $k \ge n-s$.

Let $k=n-s$. If $G \in \Gamma_{n,k}^I$ then for any vertex $i \notin I$ there is exactly one edge $[i, \sigma(i)]$ starting at it and exactly one edge $[j, \sigma(j)] = [j,i]$ finishing at it (that is, $\sigma(j) = i$). Hence $\sigma$ is a bijection $\{1 {, \dots ,} n\} \setminus I 