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

Let $${G_1} = \left( {V,\,{E_1}} \right)$$ and $${G_2} = \left( {V,\,{E_2}} \right)$$ be connected graphs on the same vertex set $$V$$ with more than two vertices. If $${G_1} \cap {G_2} = \left( {V,{E_1} \cap {E_2}} \right)$$ is not a connected graph, then the graph $${G_1} \cup {G_2} = \left( {V,{E_1} \cup {E_2}} \right)$$

$$A$$ 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?