# An example for a planar graph with different embeddings with different degree sequences of the faces?

Let $G$ be a planar graph with a planar embedding with $f$ faces. The degree of a face $f_i$ is the number $a_i$ of edges that are incident to $f_i$ (counting bridges twice). Assume that the faces $f_1$, . . . , $f_f$ are ordered such that their degrees are non descending. Consider the degreesequence ($a_1$, . . . , $a_f$ ) of the faces.

• Where is your question...? – user37238 Apr 3 '15 at 12:48

Draw a convex hexagon $ABCDEF$ and two diagonals $AC$ and $DF$. Then you have degreesequence $(3,3,4,6)$. If you draw $AC$ as an arc outside of the heaxagon, you have $(3,3,5,5)$.