1
GATE CSE 2006
+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
$$3/n$$
2
GATE CSE 2005
+2
-0.6
Which one of the following graphs is NOT planar?
A
G1
B
G2
C
G3
D
G4
3
GATE CSE 2004
+2
-0.6
The minimum number of colours required to colour the following graph, such that no two adjacent vertices are assigned the same colour, is
A
2
B
3
C
4
D
5
4
GATE CSE 2004
+2
-0.6
How many graphs on $$n$$ labeled vertices exist which have at least $$\left( {{n^2} - 3n} \right)/2\,\,\,$$ edges?
A
$${}^{\left( {{n^ \wedge }2 - n} \right)/2}{C_{\left( {{n^ \wedge }2 - 3n} \right)/2}}$$
B
$${\sum\limits_{k = 0}^{\left( {{n^ \wedge }2 - 3n} \right)/2} {{}^{\left( {{n^ \wedge }2 - n} \right)}{C_k}} }$$
C
$${}^{\left( {{n^ \wedge }2 - n} \right)/2}{C_n}$$
D
$$\sum\nolimits_{k = 0}^n {{}^{\left( {{n^ \wedge }2 - n} \right)/2}{C_k}}$$
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