If a graph has a unique MST, then its edge weights are distinct. True or false ? Justify your answer.


closed as unclear what you're asking by Yuval Filmus, Evil, Juho, Discrete lizard, David Richerby May 11 '18 at 11:50

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    $\begingroup$ You should first make some effort solving the exercise on your own. $\endgroup$ – Yuval Filmus May 10 '18 at 22:01

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.


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