Vertex identifying codes for the n-dimensional lattice

Details Vertex identifying codes for the n-dimensional lattice Vertex identifying codes for the n-dimensional lattice

2010-08-28

arxiv.org/abs/1008.4892v3

Mathematics

Combinatorics

10pp

Scientific paper

An $r$-identifying code on a graph $G$ is a set $C\subset V(G)$ such that for every vertex in $V(G)$, the intersection of the radius-$r$ closed neighborhood with $C$ is nonempty and different. Here, we provide an overview on codes for the $n$-dimensional lattice, discussing the case of 1-identifying codes, constructing a sparse code for the 4-dimensional lattice as well as showing that for fixed $n$, the minimum density of an $r$-identifying code is $\Theta(1/r^{n-1})$.

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