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Let G be a planar graph with 7 vertices, 10 edges and 3 components then the number of regions are :

a)24

b)37

c)7

d)10

Answer given : 7

How to solve this ? Is there any formulae for number of regions calculation?

The only one I know is r=e-n+2 for any planar graph.
in Graph Theory by Active (1.2k points) | 176 views
+4
Euler's formula for planar graph:

V - E + R = 1 + K

where, K-> No. of components

Solve using this, R=7
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