1
GATE CSE 2003
MCQ (Single Correct Answer)
+2
-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
A
$$3$$
B
$$4$$
C
$$5$$
D
$$6$$
2
GATE CSE 2003
MCQ (Single Correct Answer)
+2
-0.6
How many perfect matchings are there in a complete graph of 6 vertices?
A
$$15$$
B
$$24$$
C
$$30$$
D
$$60$$
3
GATE CSE 2001
MCQ (Single Correct Answer)
+2
-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?
A
$$n\left( {n - 1} \right)/2$$
B
$${2^n}$$
C
$$n!$$
D
$${2^{n\left( {n - 1} \right)/2}}$$
4
GATE CSE 1995
Subjective
+2
-0
Prove that in a finite graph, the number of vertices of odd degree is always even.
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