We have a connected undirected graph of 100 vertices and 300 edges. The weight of a minimum spanning tree of G is 500. When the weight of each edge is increased by 5, what will be the weight of the minimum spanning tree?
a. 995
b. 1000
c. 2000
d. 1995
a. 995
Since there are 100 vertices, there must be 99 edges in the MST. When weight of every edge is increased by 5, the increment in weight of the MST is 99 * 5 = 495. So, the new weight of the MST is 500 + 495, which is 995.
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