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Fault-tolerance in metric dimension of boron nanotubes lattices

The concept of resolving set and metric basis has been very successful because of multi-purpose applications both in computer and mathematical sciences. A system in which failure of any single unit, another chain of units not containing the faulty unit can replace the originally used chain is called...

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Detalles Bibliográficos
Autores principales: Hussain, Zafar, Munir, Muhammad Mobeen
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Frontiers Media S.A. 2023
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9906808/
https://www.ncbi.nlm.nih.gov/pubmed/36761392
http://dx.doi.org/10.3389/fncom.2022.1023585
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author Hussain, Zafar
Munir, Muhammad Mobeen
author_facet Hussain, Zafar
Munir, Muhammad Mobeen
author_sort Hussain, Zafar
collection PubMed
description The concept of resolving set and metric basis has been very successful because of multi-purpose applications both in computer and mathematical sciences. A system in which failure of any single unit, another chain of units not containing the faulty unit can replace the originally used chain is called a fault-tolerant self-stable system. Recent research studies reveal that the problem of finding metric dimension is NP-hard for general graphs and the problem of computing the exact values of fault-tolerant metric dimension seems to be even harder although some bounds can be computed rather easily. In this article, we compute closed formulas for the fault-tolerant metric dimension of lattices of two types of boron nanotubes, namely triangular and alpha boron. These lattices are formed by cutting the tubes vertically. We conclude that both tubes have constant fault tolerance metric dimension 4.
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spelling pubmed-99068082023-02-08 Fault-tolerance in metric dimension of boron nanotubes lattices Hussain, Zafar Munir, Muhammad Mobeen Front Comput Neurosci Neuroscience The concept of resolving set and metric basis has been very successful because of multi-purpose applications both in computer and mathematical sciences. A system in which failure of any single unit, another chain of units not containing the faulty unit can replace the originally used chain is called a fault-tolerant self-stable system. Recent research studies reveal that the problem of finding metric dimension is NP-hard for general graphs and the problem of computing the exact values of fault-tolerant metric dimension seems to be even harder although some bounds can be computed rather easily. In this article, we compute closed formulas for the fault-tolerant metric dimension of lattices of two types of boron nanotubes, namely triangular and alpha boron. These lattices are formed by cutting the tubes vertically. We conclude that both tubes have constant fault tolerance metric dimension 4. Frontiers Media S.A. 2023-01-25 /pmc/articles/PMC9906808/ /pubmed/36761392 http://dx.doi.org/10.3389/fncom.2022.1023585 Text en Copyright © 2023 Hussain and Munir. https://creativecommons.org/licenses/by/4.0/This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
spellingShingle Neuroscience
Hussain, Zafar
Munir, Muhammad Mobeen
Fault-tolerance in metric dimension of boron nanotubes lattices
title Fault-tolerance in metric dimension of boron nanotubes lattices
title_full Fault-tolerance in metric dimension of boron nanotubes lattices
title_fullStr Fault-tolerance in metric dimension of boron nanotubes lattices
title_full_unstemmed Fault-tolerance in metric dimension of boron nanotubes lattices
title_short Fault-tolerance in metric dimension of boron nanotubes lattices
title_sort fault-tolerance in metric dimension of boron nanotubes lattices
topic Neuroscience
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9906808/
https://www.ncbi.nlm.nih.gov/pubmed/36761392
http://dx.doi.org/10.3389/fncom.2022.1023585
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