Prove that if a connected, weighted graph G is input to Algorithm 10.6.4 (shown below), the output is a minimum spanning tree for G.
Input: G (a connected graph]
2. the set of all edges of G, the number of edges of G.
3a. Find an edge e in E that has maximal weight.
3b. Remove e from E and set .
3c. if the subgraph obtained when e is removed from the edge set of T is connected then remove e from the edge set of T
Output: T [a minimum spanning tree for G]
To prove that if a connected, weighted graph is the input given to following algorithm, the output will be minimum spanning tree for .
The following is the given algorithm −
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