23. Prove the following statement: If a tree T has n vertices then it has exactly n1 edges. 24. Prove that if all weights in G are different then the minimum spanning tree of G is unique. 25. Prove the following statement: Let T be a minimum spanning tree of a weighted graph G. (Denote the weight of an edge e by we.) If e=(x,y) is in G but not in T, then every edge on the path from x to y in T has weight at most we