Hello.

Suppose we have a undirected graph V. We certainly know that any vertex u can be reached from any vertex v.

If we delete vertex K and it's edges and, therefore, any vertex u losses connection with any vertex v, then K is considered to be important.

So we need to find the number of this important vertexes.

First that comes to mind is DFS, but I think there are other faster ways to solve this problem.