If G is a connected, weighted graph and no two edges of G have the same weight, does there exist a unique minimum spanning tree for G? Use the result of exercise 19 help justify your answer.
If is a connected, weighted graph and no two edges of have the same weight, then whether there exist a unique minimum spanning tree for .
Distinct minimum spanning trees.
contains a nontrivial circuit.
At least one other edge of this circuit is not in and e is the edge of least weight that is in one of the trees and not the other. Remove from to obtain a tree . Then, because is same as
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