Question: Suppose all edge weights in a graph are distinct. Does this imply that there is a unique minimum spanning tree? Discuss. Kruskal's algorithm can return

  1. Suppose all edge weights in a graph are distinct. Does this imply that there is a unique minimum spanning tree? Discuss.
  2. Kruskal's algorithm can return different spanning trees for the same input graph G depending on how it breaks the ties when edges are sorted in non-decreasing order. Is the following statement true: for every possible minimum spanning tree T of G there is a way of sorting the edges in non-decreasing order such that Kruskal's algorithm will return T? Discuss.

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