GATE CSE 2008 | Graph Theory Question 52 | Discrete Mathematics

GATE CSE 2008

MCQ (Single Correct Answer)

-0.6

$$G$$ is a graph on $$n$$ vertices and $$2n-2$$ edges. The edges of $$G$$ can be partitioned into two edge-disjoint spanning trees. Which of the following in NOT true for $$G$$?

For every subset of $$k$$ vertices, the induced subgraph has at most $$2k-2$$ edges

The minimum cut in $$G$$ has at least two edges

There are two edge-disjoint paths between every pair of vertices

There are two vertex-disjoint paths between every pair of vertices

GATE CSE 2007

MCQ (Single Correct Answer)

-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: $$Not\,\,\,every\,\,\,graph\,\,\,is\,\,\,connected?$$

$$\neg \forall x\left( {Graph\left( x \right) \Rightarrow Connected\left( x \right)} \right)$$

$$\exists x\left( {Graph\left( x \right) \wedge \neg Connected\left( x \right)} \right)$$

$$\neg \forall x\left( {\neg Graph\left( x \right) \vee Connected\left( x \right)} \right)$$

$$\forall x\left( {Graph\left( x \right) \Rightarrow \neg Connected\left( x \right)} \right)$$

GATE CSE 2007

MCQ (Single Correct Answer)

-0.6

Which of the following graphs has an Eulerian circuit?

Any $$k$$-regular graph where $$k$$ is an even number.

A complete graph on 90 vertices.

The complement of a cycle on 25 vertices.

None of the above.

GATE CSE 2006

MCQ (Single Correct Answer)

-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

$$1$$

$$n$$

$$n + 1$$

$${2^n}$$

PREVIOUS NEXT