Question: Suppose G is an undirected, connected, weighted graph such that the edges in G have distinct positive edge weights. Show that the minimum spanning tree

Suppose G is an undirected, connected, weighted graph such that the edges in G have distinct positive edge weights. Show that the minimum spanning tree for G is unchanged even if we square all the edge weights in G, that is, G has the same set of edges in its minimum spanning tree even if we replace the weight, w(e), of each edge e in G, with w(e)².

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