On the density of identifying codes in the square lattice

  • Authors:
  • Iiro Honkala;Antoine Lobstein

  • Affiliations:
  • Department of Mathematics, University of Turku, 20014 Turku, Finland;CNRS and ENST, 46 rue Barrault, 75013 Paris, France

  • Venue:
  • Journal of Combinatorial Theory Series B
  • Year:
  • 2002

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Abstract

Let G = (V, E) be an undirected graph and C a subset of vertices. If the sets Br(υ) ∩ C, υ ∈ V, are all nonempty and different, where Br(υ) denotes the set of all points within distance r from υ, 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.