Me and my friend were arguing over how to calculate the number of unique MST's in the following situation: if I have a weighted graph G with E edges and all the edges have unique weights then I know that we can have only 1 unique MST. I was thinking what will be the case if only some of the edges 2 or 3 have same weights then how many minimum spanning trees are possible in such a case? I had the idea that there are three cases if I take exactly 2 edges as having same weight: 1) both the edges are in MST 2)neither of the 2 edges is in MST 3) either of the two is in MST.
but we didnt reached an answer with this approach.