1. (20 points) Run DFS and find the discovery time and the finishing time for each vertex in this graph (use the alphabetical order starting from ' a ') 2. (20 points) Find the Strongly Connected Components (SCC) (Circle them) 3. (30 points) A binary tree is a rooted tree in which each node has at most two children. Show by induction that in any binary tree the number of nodes with two children is exactly one less than the number of leaves. 4. (30 points) directed graph G=(V,E) is semiconnected if, for all pairs of vertices u,vV , there is a path from u to v or from v to u. That is, different from the strongly connected components where you can go from u to v and then back, here you only need to either go from u to v or from v to u but don't have to get back. Give an efficient algorithm to determine whether or not G is semiconnected. Prove that your algorithm is correct and then analyze its running time. Note: to get full credit, your algorithm needs to run in O(V+E) time