Euler characteristic of a planar graph

Euler's formula states than in a finite, connected planar graph, $\mathrm{|V|}-\mathrm{|E|}+\mathrm{|F|}=2$ with $\mathrm{|V|}$ the number of vertices in the graph, $\mathrm{|E|}$ the number of edges, $\mathrm{|F|}$ the number of faces and $2$ the Euler characteristic.

Euler characteristic on Wikipedia.