1
GATE CSE 2006
MCQ (Single Correct Answer)
+2
-0.6
The $${2^n}$$ vertices of a graph $$G$$ correspond to all subsets of a set of size $$n$$, for $$n \ge 6$$. Two vertices of $$G$$ are adjacent if and only if the corresponding sets intersect in exactly two elements.

the number of vertices of degree zero in $$G$$ is

A
$$1$$
B
$$n$$
C
$$n + 1$$
D
$${2^n}$$
2
GATE CSE 2006
MCQ (Single Correct Answer)
+2
-0.6
The $${2^n}$$ vertices of a graph $$G$$ correspond to all subsets of a set of size $$n$$, for $$n \ge 6$$. Two vertices of $$G$$ are adjacent if and only if the corresponding sets intersect in exactly two elements.

The maximum degree of a vertex in $$G$$ is

A
$$\left( {\mathop 2\limits^{n/2} } \right){2^{n/2}}$$
B
$${2^{n - 2}}$$
C
$${2^{n - 3}} \times 3$$
D
$${2^{n - 1}}$$
3
GATE CSE 2006
MCQ (Single Correct Answer)
+2
-0.6
Consider the undirected graph $$G$$ defined as follows. The vertices of $$G$$ are bit strings of length $$n$$. We have an edge between vertex $$u$$ and vertex $$v$$ if and only if $$u$$ and $$v$$ differ in exactly one bit position (in other words, $$v$$ can be obtained from $$u$$ by flipping a single bit). The ratio of the choromatic number of $$G$$ to the diameter of $$G$$ is
A
$$1/{2^{n - 1}}$$
B
$$1/n$$
C
$$2/n$$
D
$$3/n$$
4
GATE CSE 2006
MCQ (Single Correct Answer)
+2
-0.6
$$F$$ is an $$n$$ $$x$$ $$n$$ real matrix. $$b$$ is an $$n$$ $$x$$ $$1$$ real vector. Suppose there are two $$n$$ $$x$$ $$1$$ vectors, $$u$$ and $$v$$ such that $$u \ne v$$, and $$Fu = b,\,\,\,\,Fv = b$$

Which one of the following statements is false?

A
Dererminant of $$F$$ is zero
B
There are an infinite number of solutions to $$Fx$$ $$=$$ $$b$$
C
There is an $$x \ne 0$$ such that $$Fx = 0$$
D
$$F$$ must have two identical rows
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