Euler's formula for connected planar graphs Euler's formula for connected planar graphs (i.e. a single connected component) states that $v-e+f=2$. State the generalization of Euler's formula for planar graphs with $k$ connected components (where $k\geq1$). 
The correct answer is $v-e+f=1+k$, but I'm not understanding the reasoning behind it. Anyone care to share some insight?

Consider 2 components... 


Both are similar components now for first excluding face f4 three faces for each component is considered so for both components
V - E + (F-1) = 1
since, V = 10, E = 12
So, for adding both we get 2V - 2E + 2F-2 = 2
Now we will consider face F4 which will be unbounded face for whole graph and will we counted once so,adding 1 on both sides
2V - 2E + 2F-1 = 3
Where, total number of vertices = 2V
total number of edges = 2E
total number of faces = 2F-1
total number of components = k = 2
so, Vtotal - Etotal + Ftotal = k+1 can be proved.
hope this helps ....
