Open Access

ARTICLE

Bounds on Fractional-Based Metric Dimension of Petersen Networks

Dalal Awadh Alrowaili¹, Mohsin Raza², Muhammad Javaid^2,*
1 Mathematics Department, College of Science, Jouf University, P.O. Box: 2014, Sakakah, Saudi Arabia
2 Department of Mathematics, School of Science, University of Management and Technology, Lahore, Pakistan
* Corresponding Author: Muhammad Javaid. Email:
(This article belongs to this Special Issue: Resolvability Parameters and their Applications)

Computer Modeling in Engineering & Sciences 2023, 135(3), 2697-2713. https://doi.org/10.32604/cmes.2023.023017

Received 05 December 2022; Accepted 15 August 2022; Issue published 23 November 2022

Abstract

The problem of investigating the minimum set of landmarks consisting of auto-machines (Robots) in a connected network is studied with the concept of location number or metric dimension of this network. In this paper, we study the latest type of metric dimension called as local fractional metric dimension (LFMD) and find its upper bounds for generalized Petersen networks GP(n, 3), where n ≥ 7. For n ≥ 9. The limiting values of LFMD for GP(n, 3) are also obtained as 1 (bounded) if n approaches to infinity.

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Keywords

Metric dimension; local fractional metric dimension; Petersen network; local resolving neighborhoods

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