$$A$$ 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 undirected graphs (not necessarily connected) can be constructed out of a given $$\,\,\,\,V = \left\{ {{v_1},\,\,{v_2},\,....,\,\,{v_n}} \right\}$$ of $$n$$ vertices?

Prove that in a finite graph, the number of vertices of odd degree is always even.

Maximum number of edges in a planar graph with $$n$$ vertices is _______ .