Before revision:  This also implies that for each twinless strong articulation point v , that is not a strong articulation point in a strongly connected digraph G, we can compute the number of TSCCs in G \setminus v. We note that the problem of computing all vertices that belong to a vertex-edge cut pair can be solved in linear-time by exploiting the structure of 3-vertex connected (triconnected)
After revision:  This also implies that for each twinless strong articulation point v which is not a strong articulation point in a strongly connected digraph G, we can compute the number of TSCCs in G \setminus v. We note that the problem of computing all vertices that belong to a vertex-edge cut pair can be solved in linear-time by exploiting the structure of 3-vertex connected (triconnected)