GATE CSE 2004 | Graph Theory Question 73 | Discrete Mathematics

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GATE CSE 2004

MCQ (Single Correct Answer)

-0.6

How many graphs on $$n$$ labeled vertices exist which have at least $$\left( {{n^2} - 3n} \right)/2\,\,\,$$ edges?

$${}^{\left( {{n^ \wedge }2 - n} \right)/2}{C_{\left( {{n^ \wedge }2 - 3n} \right)/2}}$$

$${\sum\limits_{k = 0}^{\left( {{n^ \wedge }2 - 3n} \right)/2} {{}^{\left( {{n^ \wedge }2 - n} \right)}{C_k}} }$$

$${}^{\left( {{n^ \wedge }2 - n} \right)/2}{C_n}$$

$$\sum\nolimits_{k = 0}^n {{}^{\left( {{n^ \wedge }2 - n} \right)/2}{C_k}} $$

GATE CSE 2003

MCQ (Single Correct Answer)

-0.6

How many perfect matchings are there in a complete graph of 6 vertices?

$$15$$

$$24$$

$$30$$

$$60$$

GATE CSE 2003

MCQ (Single Correct Answer)

-0.6

$$A$$ graph $$G$$ $$=$$ $$(V, E)$$ satisfies $$\left| E \right| \le \,3\left| V \right| - 6.$$ The min-degree of $$G$$ is defined as $$\mathop {\min }\limits_{v \in V} \left\{ {{{\mathop{\rm d}\nolimits} ^ \circ }egree\left( v \right)} \right\}$$. Therefore, min-degree of $$G$$ cannot be

$$3$$

$$4$$

$$5$$

$$6$$

GATE CSE 2001

MCQ (Single Correct Answer)

-0.6

how many undirected graphs (not necessarily connected) can be constructed out of a given $$\,\,\,\,V = \left\{ {{v_1},\,\,{v_2},\,....,\,\,{v_n}} \right\}$$ of $$n$$ vertices?

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

$${2^n}$$

$$n!$$

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

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