The number of distinct minimum spanning trees for the weighted graph below is _____
One can use Kirchof's theorem to get distinct minimum spanning trees .....
And it should be unweighted graph too?
$6$ is the answer.
Below diagram shows a minimum spanning tree. Highlighted (in green) are the edges picked to make the MST.
In the right side of MST, we could either pick edge ‘a’ or ‘b’. In the left side, we could either pick ‘c’ or ‘d’ or ‘e’ in MST.
There are 2 options for one edge to be picked and 3 options for another edge to be picked. Therefore, total 2*3 possible MSTs.