1. In this problem we will use weighted graph G1 as an example. The minimal spanning tree (MST) for G1 is depicted as T1. The following lemma can be used to produce T1 from G1 : Lemma Let a weighted graph G contain a cycle C. There exists an MST of G that does not contain the heaviest edge in C. (a) (1p) Prove the lemma. (b) (1p) Draw a sequence of graphs that show how T1 can be obtained from G1 by repeatedly using the above statement. When going from a graph Gi to the next graph Gi+1 : - a cycle C detected in Gi - the heaviest edge in C that is removed to obtain Gi+1 (2p) The course notes contains one algorithm for computing strongly connected components from a digraph (Tarjan's algorithm in Section 4). Find another algorithm that will also compute strongly connected components and explain how this other algorithm works. For example look on Wikipedia for strongly connected components. The algorithm of Kosaraju is one alternative algorithm. (You may present pseudocode in your explanation.)