General bounds for identifying codes in some infinite regular graphs

Irène Charon; Iiro Honkala; Olivier Hudry; Antoine Lobstein

doi:10.37236/1583

General bounds for identifying codes in some infinite regular graphs

Irène Charon
, Iiro Honkala
, Olivier Hudry
, Antoine Lobstein

Research output: Contribution to journal › Article › peer-review

Abstract

Consider a connected undirected graph G = (V, E) and a subset of vertices C. If for all vertices v ∈ V , the sets B_r(v) ∩ C are all nonempty and pairwise distinct, where B_r(v) denotes the set of all points within distance r from v, then we call C an r-identifying code. We give general lower and upper bounds on the best possible density of r-identifying codes in three infinite regular graphs.

Original language	English
Pages (from-to)	1-21
Number of pages	21
Journal	Electronic Journal of Combinatorics
Volume	8
Issue number	1 R
DOIs	https://doi.org/10.37236/1583
Publication status	Published - 1 Jan 2001

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title = "General bounds for identifying codes in some infinite regular graphs",

abstract = "Consider a connected undirected graph G = (V, E) and a subset of vertices C. If for all vertices v ∈ V , the sets Br(v) ∩ C are all nonempty and pairwise distinct, where Br(v) denotes the set of all points within distance r from v, then we call C an r-identifying code. We give general lower and upper bounds on the best possible density of r-identifying codes in three infinite regular graphs.",

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AB - Consider a connected undirected graph G = (V, E) and a subset of vertices C. If for all vertices v ∈ V , the sets Br(v) ∩ C are all nonempty and pairwise distinct, where Br(v) denotes the set of all points within distance r from v, then we call C an r-identifying code. We give general lower and upper bounds on the best possible density of r-identifying codes in three infinite regular graphs.

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General bounds for identifying codes in some infinite regular graphs

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