The full question is:
In each case, give the values of $r$, $e$, or $v$ assuming that the graph is planar. Then draw a connected planar graph with the property, if possible.
The values I was given were 6 vertices all of degree 4 and another problem with the given values 5 regions and 10 edges.
According to Euler's formula $r = e-v+2$, there should be 12 edges and 8 regions for the first problem and 7 vertices for the second problem. However I can only come up with a graph that has 7 regions for the first problem and 6 vertices in the second one. What am I doing wrong and how should I tackle drawing these problems?
