On the Metric Dimension of Generalized Petersen Multigraphs

Muhammad Imran; Muhammad Kamran Siddiqui; Rishi Naeem

doi:10.1109/ACCESS.2018.2883556

On the Metric Dimension of Generalized Petersen Multigraphs

Muhammad Imran, Muhammad Kamran Siddiqui, Rishi Naeem

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

25 Citations (Scopus)

Abstract

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 P(2n,n) have metric dimension 3 when n 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.

Original language	English
Article number	8554062
Pages (from-to)	74328-74338
Number of pages	11
Journal	IEEE Access
Volume	6
DOIs	https://doi.org/10.1109/ACCESS.2018.2883556
Publication status	Published - 2018

Keywords

Metric dimension
Möbius ladders
barycentric subdivision
basis
generalized Petersen graphs
resolving set

ASJC Scopus subject areas

Computer Science(all)
Materials Science(all)
Engineering(all)

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10.1109/ACCESS.2018.2883556

Cite this

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title = "On the Metric Dimension of Generalized Petersen Multigraphs",

abstract = "In this paper, we study the metric dimension of barycentric subdivision of M{\"o}bius ladders and the metric dimension of generalized Petersen multigraphs. We prove that the generalized Petersen multigraphs denoted by P(2n,n) have metric dimension 3 when n is even and 4 otherwise. We also study the exchange property for resolving sets of barycentric subdivisions of M{\"o}bius 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.",

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Y1 - 2018

N2 - 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 P(2n,n) have metric dimension 3 when n 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.

AB - 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 P(2n,n) have metric dimension 3 when n 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.

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KW - basis

KW - generalized Petersen graphs

KW - resolving set

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On the Metric Dimension of Generalized Petersen Multigraphs

Abstract

Keywords

ASJC Scopus subject areas

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