separating set | vertex cut set

A vertex cut, also called a vertex cut set or separating set, of a connected graph G is a subset of the vertex set S⊆V(G) such that G - S has more than one connected component. In other words, a vertex cut is a subset of vertices of a connected graph which, if removed (or "cut")--together with any incident edges--disconnects the graph (i.e., forms a disconnected graph). A vertex cut set of size 1 in a connected graph corresponds to an articulation vertex. A vertex cut of smallest size in a given connected graph G is called a minimum vertex cut and can be found in the Wolfram Language using the function FindVertexCut[G].

articulation vertex | disconnected graph | edge cut | graph toughness | k-connected graph | minimum vertex cut | vertex connectivity