Geodesic
Lower bounds for identifying codes in some infinite grids
The electronic journal of combinatorics, Tome 17 (2010)

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Zbl arXiv
An $r$-identifying code on a graph $G$ is a set $C\subset V(G)$ such that for every vertex in $V(G)$, the intersection of the radius-$r$ closed neighborhood with $C$ is nonempty and unique. On a finite graph, the density of a code is $|C|/|V(G)|$, which naturally extends to a definition of density in certain infinite graphs which are locally finite. We present new lower bounds for densities of codes for some small values of $r$ in both the square and hexagonal grids.
DOI : 10.37236/394
Classification : 05C70, 68R10, 94B65 
Ryan Martin; Brendon Stanton. Lower bounds for identifying codes in some infinite grids. The electronic journal of combinatorics, Tome 17 (2010). doi: 10.37236/394
@article{10_37236_394,
     author = {Ryan Martin and Brendon Stanton},
     title = {Lower bounds for identifying codes in some infinite grids},
     journal = {The electronic journal of combinatorics},
     year = {2010},
     volume = {17},
     doi = {10.37236/394},
     zbl = {1272.05161},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/394/}
}
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