Let $G$ be a simple $4$-regular connected graph, and suppose that $G$ is planar and has $10$ faces. (A graph is $4$-regular if all of its vertices have degree $4$.)
- Determine the number of edges of $G$.
- Determine the number of vertices of $G$.
I know about the Euler's formula $n-m+f = 2$.
Therefore with $f = 10$ it can be rearranged to: $8= -n + m$.
However I am stuck as to continue to gain exact values for $n$ and $m$.