Unless stated otherwise the input representation of graphs is adjacency list.

. Let G = (V. E) be a directed graph. Define a graph G2 = (V.E') as follows: V,-V: (u, v) E E if there is a a path of length 2 between u and v in G. . Suppose that a directed graph G is given as adjacency list. Give a O(mn)-time algorithm to compute G2. Derive the time bound. Here m is number of edges in G and n is number of vertices in G. Suppose that a directed graph G is given as adjacency matrix. Given an algorithm to compute G2. Derive the run ime of your algorithm