Given a connected, undirected graph G, edge-weighted (positive), prove thatIf G has a spanning tree T which, for each vertex r in G, is a shortest path tree from r, then G has a unique MST.I know how to show that given a T like that, it is also a MST, but how  can I show that it's unique? I tried to assume by contradiction that it isn't, but I can't see how to get a contradiction from that 
Shortest path tree from each vertex implies a unique MST?
algorithms;graphs;shortest path;minimum spanning tree