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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