Identifying and locating-dominating codes on chains and cycles

@article{Bertrand2004IdentifyingAL,
  title={Identifying and locating-dominating codes on chains and cycles},
  author={Nathalie Bertrand and Ir{\`e}ne Charon and Olivier Hudry and Antoine Lobstein},
  journal={Eur. J. Comb.},
  year={2004},
  volume={25},
  pages={969-987}
}
Consider a connected undirected graph G = (V, E), a subset of verticesC ⊆ V , and an integer r ≥ 1; for anyvertexv ∈ V , let Br (v) denote the ball of radius r centered atv, i.e., the set of all vertices within distancer from v. If for all verticesv ∈ V (respectively,v ∈ V\C), the sets Br (v) ∩ C are all nonempty and different, then we call C an r -identifying code (respectively, an r -locating-dominating code). We study the smallest cardinalities or densities of these codes in chains (finite… CONTINUE READING
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