Thread: Planar graph

Hi
I have this graph

now i should check if this graph can be planar.

v - number of vertices
e - number of edges
f - number of faces

So it's hold the theorem "If v ≥ 3 then e ≤ 3v − 6 "
v = 9, e = 15
15 ≤ 21

and should hold v - e + f = 2 from here f = 2 - v + e = 2 - 9 + 15 = 8
so f = 8 now my question is how to easily count faces (regions bounded by edges, including the outer, infinitely large region) of the graph??
thanks

You need the graph to be embedded in the plane (that is, drawn with no edges crossing) to have faces defined. Also, I think your graph is not planar. The condition you are using works like this "If the graph is planar, then " but the latter doesn't prove the first, that is "If , then the graph is planar" is WRONG.