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 _______ .

The maximum number of possible edges in an undirected graph with a vertices and $$k$$ components is _________ .