# 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.

## Source of Name

This entry was named for Leonhard Paul Euler.