Exercise · ZW-PLANAR-GRAPH-009 · ★★★ Advanced
A maximal planar graph with \(v=10\) vertices (every face a triangle) has \(e=24\) edges. How many faces does it have?
Choose one option.
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- B. 16
Explanation
\(f=2-v+e=2-10+24=16\). Check with \(3f=2e\): \(3\cdot16=48=2\cdot24\).
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.
\[v-e+f=2\]
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