Algorithms | Graph Minimum Spanning Tree | Question 8

Consider a weighted complete graph G on the vertex set {v1,v2 ,v} such that the weight of the edge (v,,v) is 2|i-j|. The weight of a minimum spanning tree of G is: (GATE CS 2006)

(A) n — 1
(B) 2n — 2
(C) nC2
(D) 2

Answer: (B)
Explanation: Minimum spanning tree of such a graph is

v1
  \
    v2
      \
       v3
         \
          v4
            .
              .
                .
                 vn
 

Weight of the minimum spanning tree
= 2|2 – 1| + 2|3 – 2| + 2|4 – 3| + 2|5 – 4| …. + 2| n – (n-1) |
= 2n – 2

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