GATE | GATE CS 2020 | Question 59

Consider a graph G=(V, E), where V = { v1,v2,…,v100 }, E={ (vi, vj) ∣ 1≤ i < j ≤ 100} and weight of the edge (vi, vj)  is ∣i–j∣. The weight of minimum spanning tree of G is ________. Note – This question was Numerical Type.

(A)

99

(B)

100

(C)

98

(D)

101

Answer: (A)

Explanation:

There are 100 vertices numbered from 1 to 100. Edges are presents in this graphs E={ (v_i, v_j) ∣ 1≤i1, v₂), (v₂, v₃), ….. (v₉₉, v₁₀₀) will have minimum weight, i.e., 1 for each edge. As we know that, there are 99 edges are possible in minimum spanning tree of 100-vertices graph. Therefore, these edges (v₁, v₂), (v₂, v₃), ….. (v₉₉, v₁₀₀) will be spanning tree for given graph. These are 99 edges with 1 cost of each. The weight of minimum spanning tree of G is 99*1 = 99. Option (A) is correct.

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