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={ (vi, vj) ∣ 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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