Möbius Strip has Euler Characteristic Zero

Theorem
Let $M$ be a Möbius Strip.

Then:
 * $\map \chi M = 0$

where $\map \chi M$ denotes the Euler characteristic of the graph $M$.

Proof
Let the number of vertices, edges and faces of $M$ be $V$, $E$ and $F$ respectively.

From Möbius Strip has no Vertices:
 * $V = 0$

From Möbius Strip has 1 Edge:
 * $E = 1$

From Möbius Strip has 1 Face:
 * $F = 1$

By definition of the Euler characteristic: