Question: Let G be a connected undirected graph with distinct positive edge weights and let T be a minimum spanning tree of G. a) Prove that

Let G be a connected undirected graph with distinct positive edge weights and let T be a minimum spanning tree of G.

a) Prove that T is the only MST of G.

b) Let G be the same graph as G except that 43 is added to the weight of each edge. Prove that T is the MST of G. Hint: Recall the definition of MST.

c) Prove that if C is any cycle in G, then the edge of C with largest weight is not in T.

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