1
GATE CSE 2007
+1
-0.3
Consider a weighted undirected graph with positive edge weights and let $$uv$$ be an edge in the graph. It is known that the shortest path from the source vertex $$s$$ to $$u$$ has weight 53 and the shortest path from $$s$$ to $$v$$ has weighted 65. Which one of the following statements is always true?
A
weight$$(u, v)$$ $$< 12$$
B
weight$$(u, v)$$ $$\le 12$$
C
weight$$(u, v)$$ $$> 12$$
D
weight$$(u, v)$$ $$\ge 12$$
2
GATE CSE 2007
+1
-0.3
The height of a binary tree is the maximum number of edges in any root to leaf path. The maximum number of nodes in a binary tree of height $$h$$ is:
A
$${2^h} - 1$$
B
$${2^{h - 1}} - 1$$
C
$${2^{h + 1}} - 1$$
D
$${2^{h + 1}}$$
3
GATE CSE 2007
+1
-0.3
The maximum number of binary trees that can be formed with three unlabeled nodes is:
A
1
B
5
C
4
D
3
4
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
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