On Vertex Identifying Codes For Infinite Lattices
نویسندگان
چکیده
An r-identifying code on a graph G is a set C ⊂ V (G) such that for every vertex in V (G), the intersection of the radius-r closed neighborhood with C is nonempty and unique. On a finite graph, the density of a code is |C|/|V (G)|, which naturally extends to a definition of density in certain infinite graphs which are locally finite. We present new lower bounds for densities of codes for some small values of r in both the square and hexagonal grids.
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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