Euler's Formula for Planar Graphs.
For any connected planar graph with \(v\) vertices, \(e\) edges and \(f\) faces, we have
\begin{equation*}
v-e + f = 2\text{.}
\end{equation*}
For any connected planar graph with \(v\) vertices, \(e\) edges and \(f\) faces, we have