Couple of weeks ago I asked this question on theory CS but I didn't get an answer. So trying it here.
I was reading combinatorial approach towards quantum correction. A lot of work in this is on finding diagonal distance of a graph. Let me add definition of diagonal distance so that this remains self-contained.
Given a labeling $L$ (a map where each vertex is is assigned 1 or 0) we define two operations on this:
$X(v,L)$: you flip labeling of vertex v that is if it was zero make it 1 if it was 1 make it 0.
$Z(v,L)$: you flip labeling of every neighbor of vertex v
Then diagonal distance is defined as length of minimal non-trivial sequence of operation so that $L$ is taken back to itself.
How is this exactly related to the quantum error correction property?