(a)
To show that the minimum spanning tree is unique but not the second best spanning tree.
(a)
Explanation of Solution
Suppose there are 4 vertices { p, q, r, s } in the following graph. Consider the edge weights and vertices as follows:
The minimum spanning tree has weight of 7 and there exists two second best minimum spanning tree having weight 8.
(b)
To prove that there exists edges ( u , v )
(b)
Explanation of Solution
T is the minimum spanning tree of graph G . Consider adding an edge that is ( u , v )
(c)
To describe an O (
(c)
Explanation of Solution
The algorithm is as follows:
Consider using dynamic
(d)
To give an efficient algorithm to compute the second-best minimum spanning tree of graph G.
(d)
Explanation of Solution
Firstly, compute the minimum spanning tree in O ( E + Vlog ( V )), this is in time O (
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