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
For any planar graph, $\text{n(no. of vertices) - e(no. of edges) + f(no. of faces) = 2}$ $f = 15 - 10 + 2= 7$ number of bounded faces $= \text{no. of faces -1}$ $= 7 -1=6$ So, the correct answer would be D
"number of bounded faces = no. of faces -1" is this formula ?
number of bounded faces = no. of faces -1 (external or unbounded face)
Gatecse
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