GATE CSE 2003 | Graph Theory Question 75 | Discrete Mathematics

Let $$G$$ be an arbitrary graph with $$n$$ nodes and $$k$$ components. If a vertex is removed from $$G$$, the number of components in the resultant graph must necessarily lie between

$$k$$ and $$n$$

$$k - 1$$ and $$k + 1$$

$$k - 1$$ and $$n - 1$$

$$k + 1$$ and $$n -k$$

GATE CSE 2002

MCQ (Single Correct Answer)

-0.3

Maximum number of edges in a n - node undirected graph without self loops is

$${n^2}$$

$$n\left( {n - 1} \right)/2$$

$$n - 1$$

$$\left( {n + 1} \right)\left( n \right)/2$$

GATE CSE 1994

MCQ (Single Correct Answer)

-0.3

The number of distinct simple graph with upto three nodes is

GATE CSE 1992

MCQ (Single Correct Answer)

-0.3

Which of the following is/are tautology?

$$\left( {a \vee b} \right) \to \left( {b \wedge c} \right)$$

$$\left( {a \wedge b} \right) \to \left( {b \vee c} \right)$$

$$\left( {a \vee b} \right) \to \left( {b \to c} \right)$$

$$\left( {a \to b} \right) \to \left( {b \to c} \right)$$

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