Let G be a simple connected planar graph with 13 vertices and 19 edges. Then, the number of faces in the planar embeddin...

Question

Let G be a simple connected planar graph with 13 vertices and 19 edges. Then, the number of faces in the planar embedding of the graph is: A. 6 B. 8 C. 9 D. 13

Accepted Answer

F = 8 -> Option B. For any connected planar graph, Euler's formula links vertices, edges and faces: V - E + F = 2. Here V = 13 and E = 19, so just solve for F: F = 2 - V + E = 2 - 13 + 19 = 8. The faces include all bounded regions plus the single unbounded outer face.