On the Metric Dimension of Generalized Petersen Multigraphs | Zendy

Muhammad Imran | Zendy; Muhammad Kamran Siddiqui | Zendy; Rishi Naeem | Zendy

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On the Metric Dimension of Generalized Petersen Multigraphs

Author(s) -

Muhammad Imran,

Muhammad Kamran Siddiqui,

Rishi Naeem

Publication year - 2018

Publication title -

ieee access

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.587

H-Index - 127

ISSN - 2169-3536

DOI - 10.1109/access.2018.2883556

Subject(s) - aerospace , bioengineering , communication, networking and broadcast technologies , components, circuits, devices and systems , computing and processing , engineered materials, dielectrics and plasmas , engineering profession , fields, waves and electromagnetics , general topics for engineers , geoscience , nuclear engineering , photonics and electrooptics , power, energy and industry applications , robotics and control systems , signal processing and analysis , transportation

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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