On the density of identifying codes in the square lattice

Abstract

Let G = (V, E) be an undirected graph and C a subset of vertices. If the sets Br(v) ∩ C, v ε 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. © 2002 Elsevier Science (USA).