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
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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