Let G be a simple connected planar graph with 13 vertices and 19 edges. Then,…
2005
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
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Correct answer: B
Use Euler's formula for connected planar graphs: V - E + F = 2
Given vertices V = 13 and edges E = 19.
Solve for the number of faces F using F = 2 - V + E.
Compute the arithmetic: 2 - 13 = -11; -11 + 19 = 8, so F = 8.
Therefore, the planar embedding has 8 faces (this count includes the outer face).
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