# Planarity in Graph Theory

I'm fighting with a homework question in Graph Theory. I think it requires Euler's formula. Can someone please give me a hand? I know the problem requires algebra, but I don't think it's that simple. Here is my question:

Let f be the number of faces in a plane diagram of a 3-regular connected planar graph. Let m and n be the number of edges and vertices, respectively. Find a formula for m in terms of n. Then find a formula for f in terms of n.

Euler's formula is: n-m+f = 2 where n = number of vertices, m = the number of edges, f = the number of faces.

$$\sum_{v \in V(G)} \deg(v) = 2 |E(G)|.$$