A planar depiction of a loop-free connected graph has 7 regions, each is a polygon. The numbers of edges on the boundaries of the regions are respectively 3,3,3,3,3,4,5. (a) Find the number of vertices of the graph. (b) Is G bipartite?
I figured out that part a) is 7 vertices. So now we have
|V| = 7 |F| = 7 and |E| = 12
so for part b) I began trying to draw sample graphs and my initial intuition is that it isn't but how do I go ahead and properly prove that?