GATE | GATE CS 2012 | Question 17
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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