Definition:Euler Characteristic of Finite Graph

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Definition

Let $G = \struct {V, E}$ be a finite graph.

Let $G$ be embedded in a surface.


The Euler characteristic of $G$ is written $\map \chi G$ and is defined as:

$\map \chi G = v - e + f$

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

  • Results about the Euler characteristic of a finite graph can be found here.


Source of Name

This entry was named for Leonhard Paul Euler.


Sources