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Use this tag whenever your question is related to minimum spanning tree (MST). An MST of a connected edge-weighted graph G is a spanning tree whose sum of edge weights is as small as possible. We usually assume $G$ is finite, simple and undirected.
5
votes
If a graph has a unique MST, then its edge weights are distinct. True or false ? Justify you...
The answer is: not necessarily.
Counterexample: consider a graph that is a tree with all of its edges the same weight. Then the only MST is the entire graph and none of the edge weights are distinct. …