On Metric Dimension in Some Hex Derived Networks †

The concept of a metric dimension was proposed to model robot navigation where the places of navigating agents can change among nodes. The metric dimension [Formula: see text] of a graph G is the smallest number k for which G contains a vertex set W, such that [Formula: see text] and every pair of v...

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Detalles Bibliográficos
Autores principales: Shao, Zehui, Wu, Pu, Zhu, Enqiang, Chen, Lanxiang
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2018
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6338904/
https://www.ncbi.nlm.nih.gov/pubmed/30597887
http://dx.doi.org/10.3390/s19010094
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author Shao, Zehui
Wu, Pu
Zhu, Enqiang
Chen, Lanxiang
author_facet Shao, Zehui
Wu, Pu
Zhu, Enqiang
Chen, Lanxiang
author_sort Shao, Zehui
collection PubMed
description The concept of a metric dimension was proposed to model robot navigation where the places of navigating agents can change among nodes. The metric dimension [Formula: see text] of a graph G is the smallest number k for which G contains a vertex set W, such that [Formula: see text] and every pair of vertices of G possess different distances to at least one vertex in W. In this paper, we demonstrate that [Formula: see text] for [Formula: see text]. This indicates that in these types of hex derived sensor networks, the least number of nodes needed for locating any other node is four.
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spelling pubmed-63389042019-01-23 On Metric Dimension in Some Hex Derived Networks † Shao, Zehui Wu, Pu Zhu, Enqiang Chen, Lanxiang Sensors (Basel) Article The concept of a metric dimension was proposed to model robot navigation where the places of navigating agents can change among nodes. The metric dimension [Formula: see text] of a graph G is the smallest number k for which G contains a vertex set W, such that [Formula: see text] and every pair of vertices of G possess different distances to at least one vertex in W. In this paper, we demonstrate that [Formula: see text] for [Formula: see text]. This indicates that in these types of hex derived sensor networks, the least number of nodes needed for locating any other node is four. MDPI 2018-12-28 /pmc/articles/PMC6338904/ /pubmed/30597887 http://dx.doi.org/10.3390/s19010094 Text en © 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Shao, Zehui
Wu, Pu
Zhu, Enqiang
Chen, Lanxiang
On Metric Dimension in Some Hex Derived Networks †
title On Metric Dimension in Some Hex Derived Networks †
title_full On Metric Dimension in Some Hex Derived Networks †
title_fullStr On Metric Dimension in Some Hex Derived Networks †
title_full_unstemmed On Metric Dimension in Some Hex Derived Networks †
title_short On Metric Dimension in Some Hex Derived Networks †
title_sort on metric dimension in some hex derived networks †
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6338904/
https://www.ncbi.nlm.nih.gov/pubmed/30597887
http://dx.doi.org/10.3390/s19010094
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