Question: The graph below is planar but not outer planar and it satisfies rank(G) = frank(G) = 3. The regions of this embedding are not bounded by primitive cycles. Thus, the converse of Proposition fails.
![633_29.png](https://secure.tutorsglobe.com/CMSImages/633_29.png)
Proposition: If G is outerplanar, then rank(G) = frank(G).