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 $f.$
Notes
 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.
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Explanations: 1
Proofs: 2 3 4
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References
Bibliography
 Aldous Joan M., Wilson Robin J.: "Graphs and Applications  An Introductory Approach", Springer, 2000