New lower bound for 2-identifying code in the square grid
نویسندگان
چکیده
منابع مشابه
New lower bound for 2-identifying code in the square grid
An r-identifying code in a graph G = (V,E) is a subset C ⊆ V such that for each u ∈ V the intersection of C and the ball of radius r centered at u is nonempty and unique. Previously, r-identifying codes have been studied in various grids. In particular, it has been shown that there exists a 2-identifying code in the square grid with density 5/29 ≈ 0.172 and that there are no 2-identifying codes...
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An r-identifying code in a graph G = (V,E) is a subset C ⊆ V such that for each u ∈ V the intersection of C and the ball of radius r centered at u is non-empty and unique. Previously, r-identifying codes have been studied in various grids. In particular, it has been shown that there exists a 2-identifying code in the hexagonal grid with density 4/19 and that there are no 2-identifying codes wit...
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We call a subset C of vertices of a graph G a (1,≤ l)-identifying code if for all subsets X of vertices with size at most l, the sets {c ∈ C|∃u ∈ X, d(u, c) ≤ 1} are distinct. The concept of identifying codes was introduced in 1998 by Karpovsky, Chakrabarty and Levitin. Identifying codes have been studied in various grids. In particular, it has been shown that there exists a (1,≤ 2)-identifying...
متن کاملOptimal Lower Bound for 2-Identifying Codes in the Hexagonal Grid
An r-identifying code in a graph G = (V,E) is a subset C ⊆ V such that for each u ∈ V the intersection of C and the ball of radius r centered at u is nonempty and unique. Previously, r-identifying codes have been studied in various grids. In particular, it has been shown that there exists a 2-identifying code in the hexagonal grid with density 4/19 and that there are no 2-identifying codes with...
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Given a graph G, an identifying code D ⊆ V (G) is a vertex set such that for any two distinct vertices v1, v2 ∈ V (G), the sets N [v1] ∩ D and N [v2] ∩ D are distinct and nonempty (here N [v] denotes a vertex v and its neighbors). We study the case when G is the infinite hexagonal grid H. Cohen et.al. constructed two identifying codes for H with density 3/7 and proved that any identifying code ...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2013
ISSN: 0166-218X
DOI: 10.1016/j.dam.2013.02.032