Definition: Face Degree
Let $G$ be a biconnected planar graph with a given planar drawing and let $f$ be any face in the drawing. Then, the degree of $f$ (denoted by $\deg f$) is the number of edges in a cycle around the boundary of $f.$
- The boundary of the infinite face is the boundary of the whole planar drawing.
- $\deg f$ depends on the drawing $\mathcal D,$ in which the face is drawn.
Proofs: 2 3 4
Thank you to the contributors under CC BY-SA 4.0!
- Aldous Joan M., Wilson Robin J.: "Graphs and Applications - An Introductory Approach", Springer, 2000