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a directed graph g = (v,e) is twinless strongly connected if it contains a strongly connected spanning subgraph without any pair of antiparallel (or twin) edges. the twinless strongly connected components (tsccs) of a directed graph g are its maximal twinless strongly connected subgraphs. these concepts have several diverse applications, such as the design of telecommunication networks and the structural stability of buildings. a vertex v ∈ v is a twinless strong articulation point of g, if the deletion of v increases the number of tsccs of g. here, we present the first linear-time algorithm that finds all the twinless strong articulation points of a directed graph. 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 undirected graph h, find all vertices v for which there exists an edge e such that h⧵{v,e} is not connected. we develop a linear-time algorithm that not only finds all such vertices v, but also computes the number of edges e such that h⧵{v,e} is not connected. 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⧵v.

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In the text, there are 34 "d"s.
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