Bounds for Codes Identifying Vertices in the Hexagonal Grid
نویسندگان
چکیده
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.
منابع مشابه
A 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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عنوان ژورنال:
- SIAM J. Discrete Math.
دوره 13 شماره
صفحات -
تاریخ انتشار 2000