Euler's formula (planar graphs)

For any connected planar drawing, vertices minus edges plus faces always equals 2.

For a connected planar graph drawn with $v$ vertices, $e$ edges, and $f$ faces (including the outer face), $v - e + f = 2$ (theorem: eulers-formula-planar-graphs) -- not to be confused with eulers-formula, the complex-exponential identity, or eulers-theorem-eulerian-graphs, the Eulerian-circuit characterization.