Geodesic
Identifying codes with small radius in some infinite regular graphs
The electronic journal of combinatorics, Tome 9 (2002)
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Let $G=(V,E)$ be a connected undirected graph and $S$ a subset of vertices. If for all vertices $v \in V$, the sets $B_r(v) \cap S$ are all nonempty and different, where $B_r(v)$ denotes the set of all points within distance $r$ from $v$, then we call $S$ an $r$-identifying code. We give constructive upper bounds on the best possible density of $r$-identifying codes in four infinite regular graphs, for small values of $r$.
DOI : 10.37236/1628
Classification : 05C70, 68R10, 94B65
Mots-clés : \(r\)-identifying code, infinite regular graphs 
@article{10_37236_1628,
     author = {Ir\`ene Charon and Olivier Hudry and Antoine Lobstein},
     title = {Identifying codes with small radius in some infinite regular graphs},
     journal = {The electronic journal of combinatorics},
     year = {2002},
     volume = {9},
     doi = {10.37236/1628},
     zbl = {0985.05033},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1628/}
}
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Irène Charon; Olivier Hudry; Antoine Lobstein. Identifying codes with small radius in some infinite regular graphs. The electronic journal of combinatorics, Tome 9 (2002). doi: 10.37236/1628

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