Möbius Strip has Euler Characteristic Zero

Theorem
Let $M$ be a Möbius Strip.

Then $χ(M)=0$, where $χ(X)$ denotes the Euler Characteristic of a graph $X$.

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

$V=0$ as Möbius Strip has no vertices.

$E=1$ as Möbius Strip has 1 edge.

$F=1$ as Möbius Strip has 1 face.

$\therefore \chi (M) = V-E+F = 0-1+1 = 0$.