1
GATE CSE 2007
MCQ (Single Correct Answer)
+2
-0.6
Let Graph$$(x)$$ be a predicate which denotes that $$x$$ is a graph. Let Connected$$(x)$$ be a predicate which denotes that $$x$$ is connected. Which of the following first order logic sentences DOES NOT represent the statement: $$Not\,\,\,every\,\,\,graph\,\,\,is\,\,\,connected?$$
A
$$\neg \forall x\left( {Graph\left( x \right) \Rightarrow Connected\left( x \right)} \right)$$
B
$$\exists x\left( {Graph\left( x \right) \wedge \neg Connected\left( x \right)} \right)$$
C
$$\neg \forall x\left( {\neg Graph\left( x \right) \vee Connected\left( x \right)} \right)$$
D
$$\forall x\left( {Graph\left( x \right) \Rightarrow \neg Connected\left( x \right)} \right)$$
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 number of vertices of degree zero in $$G$$ is

A
$$1$$
B
$$n$$
C
$$n + 1$$
D
$${2^n}$$
3
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
$${2^{n - 1}}$$
4
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
$$3/n$$
GATE CSE Subjects
Software Engineering
Web Technologies
EXAM MAP
Medical
NEET
Graduate Aptitude Test in Engineering
GATE CSEGATE ECEGATE EEGATE MEGATE CEGATE PIGATE IN
Civil Services
UPSC Civil Service
Defence
NDA
CBSE
Class 12