On the Metric Dimension of Generalized Petersen Multigraphs

In this paper, we study the metric dimension of barycentric subdivision of Möbius ladders and the metric dimension of generalized Petersen multigraphs. We prove that the generalized Petersen multigraphs denoted by <inline-formula> <tex-math notation="LaTeX">$P(2n,n)$...

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Autores principales:	Muhammad Imran, Muhammad Kamran Siddiqui, Rishi Naeem
Formato:	article
Lenguaje:	EN
Publicado:	IEEE 2018
Materias:	Metric dimension basis resolving set barycentric subdivision Möbius ladders generalized Petersen graphs Electrical engineering. Electronics. Nuclear engineering TK1-9971
Acceso en línea:	https://doaj.org/article/1147376d8c65451287f91897c0cb7fcd
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spelling	oai:doaj.org-article:1147376d8c65451287f91897c0cb7fcd2021-11-19T00:02:41ZOn the Metric Dimension of Generalized Petersen Multigraphs2169-353610.1109/ACCESS.2018.2883556https://doaj.org/article/1147376d8c65451287f91897c0cb7fcd2018-01-01T00:00:00Zhttps://ieeexplore.ieee.org/document/8554062/https://doaj.org/toc/2169-3536In this paper, we study the metric dimension of barycentric subdivision of Möbius ladders and the metric dimension of generalized Petersen multigraphs. We prove that the generalized Petersen multigraphs denoted by <inline-formula> <tex-math notation="LaTeX">$P(2n,n)$ </tex-math></inline-formula> have metric dimension 3 when <inline-formula> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula> is even and 4 otherwise. We also study the exchange property for resolving sets of barycentric subdivisions of Möbius ladders and generalized Petersen multigraphs and prove that the exchange property of the bases in a vector space does not hold for minimal resolving sets of these graphs.Muhammad ImranMuhammad Kamran SiddiquiRishi NaeemIEEEarticleMetric dimensionbasisresolving setbarycentric subdivisionMöbius laddersgeneralized Petersen graphsElectrical engineering. Electronics. Nuclear engineeringTK1-9971ENIEEE Access, Vol 6, Pp 74328-74338 (2018)
institution	DOAJ
collection	DOAJ
language	EN
topic	Metric dimension basis resolving set barycentric subdivision Möbius ladders generalized Petersen graphs Electrical engineering. Electronics. Nuclear engineering TK1-9971
spellingShingle	Metric dimension basis resolving set barycentric subdivision Möbius ladders generalized Petersen graphs Electrical engineering. Electronics. Nuclear engineering TK1-9971 Muhammad Imran Muhammad Kamran Siddiqui Rishi Naeem On the Metric Dimension of Generalized Petersen Multigraphs
description	In this paper, we study the metric dimension of barycentric subdivision of Möbius ladders and the metric dimension of generalized Petersen multigraphs. We prove that the generalized Petersen multigraphs denoted by <inline-formula> <tex-math notation="LaTeX">$P(2n,n)$ </tex-math></inline-formula> have metric dimension 3 when <inline-formula> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula> is even and 4 otherwise. We also study the exchange property for resolving sets of barycentric subdivisions of Möbius ladders and generalized Petersen multigraphs and prove that the exchange property of the bases in a vector space does not hold for minimal resolving sets of these graphs.
format	article
author	Muhammad Imran Muhammad Kamran Siddiqui Rishi Naeem
author_facet	Muhammad Imran Muhammad Kamran Siddiqui Rishi Naeem
author_sort	Muhammad Imran
title	On the Metric Dimension of Generalized Petersen Multigraphs
title_short	On the Metric Dimension of Generalized Petersen Multigraphs
title_full	On the Metric Dimension of Generalized Petersen Multigraphs
title_fullStr	On the Metric Dimension of Generalized Petersen Multigraphs
title_full_unstemmed	On the Metric Dimension of Generalized Petersen Multigraphs
title_sort	on the metric dimension of generalized petersen multigraphs
publisher	IEEE
publishDate	2018
url	https://doaj.org/article/1147376d8c65451287f91897c0cb7fcd
work_keys_str_mv	AT muhammadimran onthemetricdimensionofgeneralizedpetersenmultigraphs AT muhammadkamransiddiqui onthemetricdimensionofgeneralizedpetersenmultigraphs AT rishinaeem onthemetricdimensionofgeneralizedpetersenmultigraphs
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On the Metric Dimension of Generalized Petersen Multigraphs

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