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Lemma: Handshaking Lemma for Planar Graphs

Let G(V,E) be a biconnected planar graph with a given planar drawing \mathcal D. Then the sum of face degrees in the drawing is equal to twice the number of edges, formally

\sum_{f\in \mathcal D}\deg (f)=2\cdot|E|.

Proofs: 1

Proofs: 1 2


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References

Bibliography

  1. Aldous Joan M., Wilson Robin J.: "Graphs and Applications - An Introductory Approach", Springer, 2000