Simple connected maximal planar graph with 100 vertices.
so , V=100
say no of faces =f
now, Here we assume f>=3
The sum of the degrees of the regions is equal to twice the number of edges. But each region must have degree ≥ 3. So we have 2e ≥ 3f.
by euler formula we know that ,
e=v+f-2.
2(v+f-2)>=3f
or, 2v+2f-4>=3f
or 2v-4>=f
now putting v=100 we get ,
f<=196.
so maximum number of faces possible is 196.
