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On Codes Identifying Vertices in the Two-Dimensional Square Lattice with Diagonals
February 2001 (vol. 50 no. 2)
pp. 174-176
ASCII Text
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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.
 
 
BibTex
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@article{ 10.1109/12.908992,
author = {Gérard D. Cohen and Iiro Honkala and Antoine Lobstein and Gilles Zémor},
title = {On Codes Identifying Vertices in the Two-Dimensional Square Lattice with Diagonals},
journal ={IEEE Transactions on Computers},
volume = {50},
number = {2},
issn = {0018-9340},
year = {2001},
pages = {174-176},
doi = {http://doi.ieeecomputersociety.org/10.1109/12.908992},
publisher = {IEEE Computer Society},
address = {Los Alamitos, CA, USA},
}
 
 
RefWorks Procite/RefMan/Endnote
x 
 
TY - JOUR
JO - IEEE Transactions on Computers
TI - On Codes Identifying Vertices in the Two-Dimensional Square Lattice with Diagonals
IS - 2
SN - 0018-9340
SP174
EP176
EPD - 174-176
A1 - Gérard D. Cohen,
A1 - Iiro Honkala,
A1 - Antoine Lobstein,
A1 - Gilles Zémor,
PY - 2001
KW - Graph
KW - square lattice
KW - code
KW - identifying code.
VL - 50
JA - IEEE Transactions on Computers
ER -
 

Abstract—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 $B(v) \cap C$ consisting of all elements of $C$ within distance one from the vertex $v$ are different. We also require that the sets $B(v) \cap C$ 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.

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Index Terms:
Graph, square lattice, code, identifying code.
Citation:
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, Feb. 2001, doi:10.1109/12.908992
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