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) 3
(B) 4
(C) 5
(D) 6

Answer: (D)

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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