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Identifying and locating-dominating codes on chains and cycles

descriptionPublicationkeyboard_double_arrow_right Article 01 Oct 2004 English Publisher:Elsevier BVJournal:European Journal of Combinatorics, volume 25, pages 969-987 (issn: 0195-6698, Copyright policy )
Authors: Nathalie Bertrand 0001; Irène Charon; Olivier Hudry; Antoine Lobstein;

doi: 10.1016/j.ejc.2003.12.013

Identifying and locating-dominating codes on chains and cycles

Abstract

On a connected undirected graph \((V,E)\), an \(r\)-identifying code is a subset \(C\) of \(V\) such that the sets \(B_r(v)\cap C\) are distinct and nonempty for all \(v\in V\). A code is \(r\)-locating-dominating if this is true for all \(v\in V\backslash C\). This paper determines the minimum sizes (or densities) in many cases for these codes on finite and infinite chains and cycles.

Related Organizations
Keywords

Bounds on codes, Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.), Computational Theory and Mathematics, Other types of codes, \(r\)-identifying code, Geometry and Topology, \(r\)-locating-dominating code, Theoretical Computer Science

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    selected citations
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    This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    		 69
    popularity
    This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
    		 Top 10%
    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
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    impulse
    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
69
Top 10%
Top 1%
Top 10%
hybrid