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

Which one of the following graphs is NOT planar?

The minimum number of colours required to colour the following graph, such that no two adjacent vertices are assigned the same colour, is

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