How to find total number of minimum spanning trees in a graph?

Question

I don\'t want to find all the minimum spanning trees but I want to know how many of them are there, here is the method I considered:

• Find one minimum spanning tree

Answer 1

MST and their count in a graph are well-studied. See for instance: http://www14.informatik.tu-muenchen.de/konferenzen/Jass08/courses/1/pieper/Pieper_Paper.pdf.