Exercise · ZW-PLANAR-GRAPH-002 · ★☆☆ Basic
A connected planar graph has \(v=8\) vertices and \(e=12\) edges. How many faces (counting the outer one) does its drawing have?
Choose one option.
Show answer
- B. 6
Explanation
By Euler's formula \(v-e+f=2\): \(f=2-8+12=6\).
Review the concept: Planar graph
A planar graph is a graph that can be drawn in the plane with no crossing edges; such a drawing, for \(v\) vertices and \(e\) edges, splits the plane into \(f\) faces.
\[v-e+f=2\]
More practice problems: planar graph
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