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:
"G is a connected graph", "on the plane" => so the graph is planar and connected
Theorem 1 (Euler's Formula) Let G be a connected planar graph, and let n, m and f denote, respectively, the numbers of vertices, edges, and faces in a plane drawing of G. Then n - m + f = 2.
10 - 15 + f =2 => f =7
One of the face is non bounded so, answer is 6.
Ref: http://www.personal.kent.edu/~rmuhamma/GraphTheory/MyGraphTheory/planarity.htm
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