On codes identifying vertices in the two-dimensional square lattice with diagonals



: Cohen GD, Honkala I, Lobstein A, Zemor G

Publisher: IEEE COMPUTER SOC

: 2001

: IEEE Transactions on Computers

: IEEE TRANSACTIONS ON COMPUTERS

: IEEE T COMPUT

: 50

: 2

: 174

: 176

: 3

: 0018-9340

DOI: https://doi.org/10.1109/12.908992


Fault diagnosis of multiprocessor systems motivates the following graph-theoretic definition. A subset C of points in an undirected graph G = (V, E) is called an identifying code if the sets B(upsilon) boolean AND C consisting of all elements of C within distance one from the vertex upsilon are different. We also require that the sets B(upsilon) boolean AND C are all nonempty. We take G 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.



Last updated on 2024-26-11 at 21:59