Category:Definitions/Genera of Surfaces

This category contains definitions related to Genera of Surfaces.
Related results can be found in Category:Genera of Surfaces.

Let $S$ be a surface.

Let $G = \struct {V, E}$ be a graph which is embedded in $S$.

Let $G$ be such that each of its faces is a simple closed curve.

Let $\map \chi G = v - e + f = 2 - 2 p$ be the Euler characteristic of $G$ where:

$v = \size V$ is the number of vertices

$e = \size E$ is the number of edges

$f$ is the number of faces.

Then $p$ is known as the genus of $S$.