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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...
Autores principales: | , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Frontiers Media S.A.
2023
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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. |
format | Online Article Text |
id | pubmed-9906808 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2023 |
publisher | Frontiers Media S.A. |
record_format | MEDLINE/PubMed |
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 |
work_keys_str_mv | AT hussainzafar faulttoleranceinmetricdimensionofboronnanotubeslattices AT munirmuhammadmobeen faulttoleranceinmetricdimensionofboronnanotubeslattices |