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Consider a connected undirected graph G = (V, E), a subset of vertices C ⊆ V , and an integer r ≥ 1; for any vertex v ∈ V , let B r (v) denote the ball of radius r centered at v, i.e., the set of all vertices within distance r from v. If for all vertices v ∈ V (respectively, v ∈ V \C), the sets B r (v) ∩ C are all nonempty and different, then we call C an(More)
Let G = (V, E) be a connected undirected graph and S a subset of vertices. If for all vertices v ∈ V , the sets B r (v) ∩ 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(More)
Consider a connected undirected graph G = (V, E) and a subset of vertices C. If for all vertices v ∈ V , the sets B r (v) ∩ C are all nonempty and pairwise distinct, where B r (v) denotes the set of all points within distance r from v, then we call C an r-identifying code. We give general lower and upper bounds on the best possible density of r-identifying(More)