\begin{definition}[Definition:Euler Characteristic of Finite Graph]
Let $X = \struct {V, E}$ be a graph.
Let $X$ be embedded in a surface.
The '''Euler characteristic''' of $X$ is written $\map \chi X$ and is defined as:
:$\map \chi x = v - e + f$
where:
:$v = \size V$ is the number of vertices
:$e = \size E$ is the number of edges
:$f$ is the number of faces.
\end{definition}