Issue No.02 - February (2001 vol.50)
DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/12.908992
<p><b>Abstract</b>—Fault diagnosis of multiprocessor systems motivates the following graph-theoretic definition. A subset <tmath>$C$</tmath> of points in an undirected graph <tmath>$G=(V,E)$</tmath> is called an identifying code if the sets <tmath>$B(v) \cap C$</tmath> consisting of all elements of <tmath>$C$</tmath> within distance one from the vertex <tmath>$v$</tmath> are different. We also require that the sets <tmath>$B(v) \cap C$</tmath> are all nonempty. We take <tmath>$G$</tmath> to be the infinite square lattice with diagonals and show that the density of the smallest identifying code is at least 2/9 and at most 4/17.</p>
Graph, square lattice, code, identifying code.
Gérard D. Cohen, Iiro Honkala, Antoine Lobstein, Gilles Zémor, "On Codes Identifying Vertices in the Two-Dimensional Square Lattice with Diagonals", IEEE Transactions on Computers, vol.50, no. 2, pp. 174-176, February 2001, doi:10.1109/12.908992