2002
DOI: 10.1006/jctb.2001.2106
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Abstract: Let G=(V, E) be an undirected graph and C a subset of vertices. If the sets B r (v) 5 C, v ¥ V, are all nonempty and different, where B r (v) denotes the set of all points within distance r from v, we call C an r-identifying code. We give bounds on the best possible density of r-identifying codes in the two-dimensional square lattice. © 2002 Elsevier Science (USA)

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Cited by 28 publications
(36 citation statements)
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“…It is easy to verify that the code C illustrated in Fig. 5 is (1, ≤ 1 ∈ I (F), then b ∈ F. Assume that (7,8) ∈ I (F). If now (9,6) or (9, 7) does not belong to I (F), then a ∈ F. Suppose then that these points are in I (F).…”
Section: Theoremmentioning
confidence: 99%
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“…It is easy to verify that the code C illustrated in Fig. 5 is (1, ≤ 1 ∈ I (F), then b ∈ F. Assume that (7,8) ∈ I (F). If now (9,6) or (9, 7) does not belong to I (F), then a ∈ F. Suppose then that these points are in I (F).…”
Section: Theoremmentioning
confidence: 99%
“…If now (9,6) or (9, 7) does not belong to I (F), then a ∈ F. Suppose then that these points are in I (F). One element of F covers (7,8). If (9, 5) / ∈ I (F), we know that b ∈ F, and if (9, 5) ∈ I (F), we obtain a ∈ F (and (9, 6) ∈ F).…”
Section: Theoremmentioning
confidence: 99%
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“…For special values of r, this graph has been considered in many papers, for example, [1,3,6,8,9]. For related results, see [2,12].…”
Section: Introductionmentioning
confidence: 99%
“…Such identifying codes were introduced in Karpovsky, Chakrabarty and Levitin [11]. Many results have been obtained about the identifying codes, for instance in the triangular lattice, the square and king grids and the hexagonal mesh, see, e.g., [1][2][3][6][7][8][9][10], and their references. For the closely related problem of locating-dominating sets, in which the sets I(v) are required to be nonempty and pairwise different for v / ∈ C, we refer to [4,12,14,15].…”
Section: Introductionmentioning
confidence: 99%