Let G be a connected, weighted, undirected graph in which all the edges have distinct weights. Prove that G has a unique MST (minimum spanning tree), ie., there is precisely one tree that achieves the minimum weight. [Note: this is a well-known fact (and you wil likely find solutions onl). But it is one you should know, and is not too hard to prove. Hint: Suppose there are two minimum spanning trees T and T ,, and suppose their edges are ei , e2 , en- and fi, 2,.. .fn-1 respectively, in increasing order of weights. Consider the first i for which e, fi and try to arrive at a contradiction. ]