Question

Let G be a simple undirected planar graph on 10 vertices with 15 edges. If G is a connected graph, then the number of bounded faces in any embedding of G on the plane is equal to

• A. 3
• B. 4
• C. 5
• D. 6

Answer 1

The correct option is D 6

n = 10
e = 15

In a simple connected planar graph, Euler's formula gives the total number of regions as
e - n + 2 = 15 - 10 + 2 = 7

Out of this, one region is unbounded and the other 6 are bounded.

So correct answer is 6, which is option (d).