Definition:Euler Characteristic of Finite Graph

Definition
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.

Also see

 * Euler's Theorem for Planar Graphs


 * Euler Polyhedron Formula