[Sarmi]

What does it mean when minimum spanning tree is unique?

[AndrewD95]

It means there is no other the same, so if you were doing prims algorithm you may have had to choose between 2 arcs of the same length at one point, this would mean it is not unique.

[AndrewD95]

good luck if you are doing the exam tomorrow

[Sarmi]

Okai....Thank You

[Implication]

If a minimum spanning tree is unique, it is the only minimum spanning tree. As AndrewD95 says, you will sometimes have a choice between two arcs of equal weight. Sometimes, your minimum spanning tree will vary with which of these arcs you choose. Unless this is the case, your minimum spanning tree is unique.