An Optimal Strongly Identifying Code in the Infinite Triangular Grid
نویسندگان
چکیده
منابع مشابه
An Optimal Strongly Identifying Code in the Infinite Triangular Grid
Assume that G = (V,E) is an undirected graph, and C ⊆ V . For every v ∈ V , we denote by I(v) the set of all elements of C that are within distance one from v. If the sets I(v) \ {v} for v ∈ V are all nonempty, and, moreover, the sets {I(v), I(v) \ {v}} for v ∈ V are disjoint, then C is called a strongly identifying code. The smallest possible density of a strongly identifying code in the infin...
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For a graph, G, and a vertex v ∈ V (G), let N [v] be the set of vertices adjacent to and including v. A set D ⊆ V (G) is a vertex identifying code if for any two distinct vertices v1, v2 ∈ V (G), the vertex sets N [v1]∩D and N [v2]∩D are distinct and non-empty. We consider the minimum density of a vertex identifying code for the infinite hexagonal grid. In 2000, Cohen et al. constructed two cod...
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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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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2010
ISSN: 1077-8926
DOI: 10.37236/363