(the new batch)
My response on this topic from a math.stackexchange post.
Create a graph defined on all $(x,y)$ pairs for $x,y\in\mathbb Z$ as follows: $(x,y)$ is a coordinate pair referring to one vertex/node, all of which are laid out in a grid graph. Every vertex $(x,y)$ has an edge leading either north (up, $+y$) or west (left, $-x$). If $\gcd(x,y)=1$, that is, $x$ is coprime to…