New bounds on the minimum density of an identifying code for the infinite hexagonal grid
نویسندگان
چکیده
منابع مشابه
New Bounds on the Minimum Density of a Vertex Identifying Code for the Infinite Hexagonal Grid
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...
متن کاملA New Lower Bound on the Density of Vertex Identifying Codes for the Infinite Hexagonal Grid
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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15 صفحه اولBounds for Codes Identifying Vertices in the Hexagonal Grid
In an undirected graph G = (V; E) a subset C V is called an identifying code, if the sets B1 (v) \ C consisting of all elements of C within distance one from the vertex v are nonempty and diierent. We take G to be the innnite hexagonal grid, and show that the density of any identifying code is at least 16=39 and that there is an identifying code of density 3=7.
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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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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2013
ISSN: 0166-218X
DOI: 10.1016/j.dam.2013.06.002