1
GATE CSE 2011
MCQ (Single Correct Answer)
+2
-0.6
An undirected graph G(V, E) contains n ( n > 2 ) nodes named v1 , v2 ,….vn. Two nodes vi , vj are connected if and only if 0 < |i – j| <= 2. Each edge (vi, vj ) is assigned a weight i + j. A sample graph with n = 4 is shown below. What will be the cost of the minimum spanning tree (MST) of such a graph with n nodes?
A
$${1 \over {12}}(11{n^2} - 5n)$$
B
$${n^2}{\rm{ - }}\,n + 1$$
C
6n – 11
D
2n + 1
2
GATE CSE 2011
MCQ (Single Correct Answer)
+2
-0.6
An undirected graph G(V, E) contains n ( n > 2 ) nodes named v1 , v2 ,….vn. Two nodes vi , vj are connected if and only if 0 < |i – j| <= 2. Each edge (vi, vj ) is assigned a weight i + j. A sample graph with n = 4 is shown below. 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
3
GATE CSE 2010
MCQ (Single Correct Answer)
+2
-0.6
Consider a complete undirected graph with vertex set {0, 1, 2, 3, 4}. Entry W(ij) in the matrix W below is the weight of the edge {i, j}. $$w = \left( {\matrix{ 0 & 1 & 8 & 1 & 4 \cr 1 & 0 & {12} & 4 & 9 \cr 8 & {12} & 0 & 7 & 3 \cr 1 & 4 & 7 & 0 & 2 \cr 4 & 9 & 3 & 2 & 0 \cr } } \right)$$$What is the minimum possible weight of a spanning tree T in this graph such that vertex 0 is a leaf node in the tree T? A 7 B 8 C 9 D 10 4 GATE CSE 2010 MCQ (Single Correct Answer) +2 -0.6 Consider a complete undirected graph with vertex set {0, 1, 2, 3, 4}. Entry W(ij) in the matrix W below is the weight of the edge {i, j}. $$w = \left( {\matrix{ 0 & 1 & 8 & 1 & 4 \cr 1 & 0 & {12} & 4 & 9 \cr 8 & {12} & 0 & 7 & 3 \cr 1 & 4 & 7 & 0 & 2 \cr 4 & 9 & 3 & 2 & 0 \cr } } \right)$$$ 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
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