Articulation point

Articulation point — точка сочленения графа, разделяющая вершина, шарнир.

A vertex [math]\displaystyle{ v \in V }[/math] is an articulation point of a graph [math]\displaystyle{ \,G = (V,E) }[/math] if [math]\displaystyle{ G(V \setminus \{v\}) }[/math] is disconnected. A graph [math]\displaystyle{ \,G }[/math] is 2-connected if [math]\displaystyle{ \,G }[/math] has no articulation points. The maximal 2-connected subgraphs of [math]\displaystyle{ \,G }[/math] are the blocks of [math]\displaystyle{ \,G }[/math].

Other names are Cutpoint, Cutting vertex, Cutvertex.