Definition:Genus of Surface

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Definition

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 $S$.


Also see

  • Results about genera of surfaces can be found here.


Linguistic Note

The plural of genus is genera.


Sources