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GATE | GATE CS 2012 | Question 17

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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)

6
 

(B)

5
 

(C)

4
 

(D)

3
 



Answer: (A)

Explanation:

If the graph is planar, then it must follow below Euler’s Formula for planar graphs
 

v - e + f = 2
v is number of vertices
e is number of edges
f is number of faces including bounded and unbounded
10 - 15 + f = 2
f = 7
There is always one unbounded face, so the number of bounded faces =  6
 


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Last Updated : 28 Jun, 2021
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