A plane connected graph has 22 corners (eng. Vertices) and all surfaces the graph divides the plane (also the external, unlimited surface) has just 4 edges
Find all possible values for the number of edges in the graph.
I get all surfaces to r = 4*e it is wrong how can i get the connection beetween surfaces and edges
Let $V$ be the number of vertices, $F$ the number of faces and $E$ the number of edges of your graph. You have that $V = 22$ and condition that all faces have four edges can be translated into $2E = 4F$, since $4F$ counts every edge of your graph twice. Using Euler's relation, we get $$2 = V - E + F = 22 - E + \frac{E}{2} \ \implies \ E = 40.$$