Discussion

G is a planar graph with V-vertices, E-edges and F-faces. If V = 5, E = 8, then F =

Answer: A

The graph has 5 faces.

Euler's formula holds for every connected planar graph:

\[ \begin{aligned} V - E + F &= 2 \\ 5 - 8 + F &= 2 \\ F &= 5 \end{aligned} \]

The count includes the unbounded outer face. 3 is just E - V, which leaves the 2 out of the formula, and 6 and 7 do not satisfy it for these values.

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