The length of the path from v5 to v6 in the MST of previous question with n = 10 is
(A) 11
(B) 25
(C) 31
(D) 41

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

In the graph given in above question question, what is the minimum possible weight of a path P from vertex 1 to vertex 2 in this graph such that P contains at most 3 edges?
(A) 7
(B) 8
(C) 9
(D) 10

Let G be an undirected connected graph with distinct edge weight. Let emax be the edge with maximum weight and emin the edge with minimum weight. Which of the following statements is false? (GATE CS 2000)
(A) Every minimum spanning tree of G must contain emin
(B) If emax is in a minimum spanning tree, then its removal must disconnect G
(C) No minimum spanning tree contains emax
(D) G has a unique minimum spanning tree

An undirected graph G has n nodes. Its adjacency matrix is given by an n × n square matrix whose (i) diagonal elements are 0‘s and (ii) non-diagonal elements are 1‘s. which one of the following is TRUE?
(A) Graph G has no minimum spanning tree (MST)
(B) Graph G has a unique MST of cost n-1
(C) Graph G has multiple distinct MSTs, each of cost n-1
(D) Graph G has multiple spanning trees of different costs

We use dynamic programming approach when
(A) We need an optimal solution
(B) The solution has optimal substructure
(C) The given problem can be reduced to the 3-SAT problem
(D) It’s faster than Greedy

In the above question, which entry of the array X, if TRUE, implies that there is a subset whose elements sum to W?
(A) X[1, W]
(B) X[n ,0]
(C) X[n, W]
(D) X[n -1, n]

The subset-sum problem is defined as follows. Given a set of n positive integers, S = {a1 ,a2 ,a3 ,…,an} and positive integer W, is there a subset of S whose elements sum to W? A dynamic program for solving this problem uses a 2-dimensional Boolean array X, with n rows and W+1 columns. X[i, j],1 <= i <= n, 0 <= j <= W, is TRUE if and only if there is a subset of {a1 ,a2 ,…,ai} whose elements sum to j. Which of the following is valid for 2 <= i <= n and ai <= j <= W?
(A) X[i, j] = X[i – 1, j] ∨ X[i, j -ai]
(B) X[i, j] = X[i – 1, j] ∨ X[i – 1, j – ai]
(C) X[i, j] = X[i – 1, j] ∧ X[i, j – ai]
(D) X[i, j] = X[i – 1, j] ∧ X[i -1, j – ai]