3. (20 Points) Let G be an undirected connected graph and T its DFS tree. Let v be a non-root vertex of T. Prove that v is a cut vertex of G if and only if v has a child s such that there is no back edge from s or any descendant of s to a proper ancestor of v. 3. (20 Points) Let G be an undirected connected graph and T its DFS tree. Let v be a non-root vertex of T. Prove that v is a cut vertex of G if and only if v has a child s such that there is no back edge from s or any descendant of s to a proper ancestor of v