1
GATE CSE 2006
+1
-0.3
If all the edge weights of an undirected graph are positive, then any subject of edges that connects all the vertices and has minimum total weight is a
A
Hamiltonian cycle
B
grid
C
hypercube
D
tree
2
GATE CSE 2006
+1
-0.3
Consider a weighted complete graph $$G$$ on the vertex set $$\left\{ {{v_1},\,\,\,{v_2},....,\,\,\,{v_n}} \right\}$$ such that the weight of the edge $$\left( {{v_i},\,\,\,\,{v_j}} \right)$$ is $$2\left| {i - j} \right|$$. The weight of a minimum spanning tree of $$G$$ is
A
$$n - 1$$
B
$$2n - 2$$
C
$$\left( {\matrix{ n \cr 2 \cr } } \right)$$
D
$${n^2}$$
3
GATE CSE 2005
+1
-0.3
Let $$G$$ be a simple connected planar graph with 13 vertices and 19 edges. Then, the number of faces in the planar embedding of the graph is:
A
6
B
8
C
9
D
13
4
GATE CSE 2005
+1
-0.3
Let $$G$$ be the simple graph with 20 vertices and 100 edges. The size of the minimum vertex cover of $$G$$ is 8. Then, the size of the maximum independent set of $$G$$ is:
A
12
B
8
C
Less than 8
D
More than 12
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