GATE | GATE-CS-2015 (Set 3) | Question 50

Let G be 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 of G is increased by five, the weight of a minimum spanning tree becomes ________.
(A) 1000
(B) 995
(C) 2000
(D) 1995


Answer: (B)

Explanation: Since there are 100 vertices, there must be 99 edges in Minimum Spanning Tree (MST).

When weight of every edge is increased by 5, the increment in weight of MST is = 99 * 5 = 495

So new weight of MST is 500 + 495 which is 995

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