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

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

$$A$$ 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

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