On the Density of Identifying Codes in the Square Lattice

Let G=(V, E) be an undirected graph and C a subset of vertices. If the sets Br(v)∩C, v∈V, are all nonempty and different, where Br(v) denotes the set of all points within distance r from v, we call C an r-identifying code. We give bounds on the best possible density of r-identifying codes in the two-dimensional square lattice.