# Tag Info

Let's take an $n\times n$ mesh (with $N=n^2$ unknowns) and think about whether you can enumerate them in such a way that you end up with a bandwidth less than $m=n=\sqrt{N}$? You get this bandwidth with a 5-point stencil if you enumerate the first row left to right, then the next row left to right, etc. In that case, each degree of freedom $i$ couples with $... 1 I mean I think you clearly showed the graph$G$can induce a metric, namely define$d_G(u,v)$as the shortest path from$u \in V(G)$to$v \in V(G)$and you can readily show the three properties you define. The graph$G_c\$ is not even needed in this discussion, as far as I can tell. Here is a link to some document that describes a similar claim.