How can I count the number of faces in $K_2$?

Question

I studied that in $K_2$ we have $V=2$, $E=1$, and $F=1$, and in $K_3$, we have $V=3$, $E=3$, and $F=2.$

But where is the face in $K_2$? There is only one line in there.

Answer 1

As ArtW says in the comments, you can define the faces of a planar embedding of a graph $G$ to be the connected components of the plane minus the graph ($\mathbb{R}^2-G$). Since any embedding of $K_2$ in the plane is just a line, there is a single connected component, so $K_2$ has one face.