Before revision:  We show that the computation of twinless strong articulation points reduces to the following problem in undirected graphs, which may be of independent interest: Given a 2-vertex-connected (biconnected) undirected graph H, find all vertices v that belong to a vertex-edge cut pair , i.e., for which there exists an edge e such that H \setminus \{v,e\} is not connected.
After revision:  We show that the computation of twinless strong articulation points reduces to the following problem in undirected graphs, which may be of independent interest: Given a 2-vertex-connected (biconnected) undirected graph H, find all vertices v that belong to a vertex-edge cut-pair , i.e., for which there exists an edge e such that H \setminus \{v,e\} is not connected.