A weights invariant.
Exercise 23.1-8
It is to show that all minimum spanning trees have the same multi-set of weights. For instance, in a graph with 5 vertices you can't have one minimum spanning tree with weights 1, 2, 2, 4 and another with weights 1, 1, 3, 4.
Remark: A corollary of this exercise is that if all the edge weights of a graph are distinct from each other, then there is a unique minimum spanning tree for that graph.