Open Access
ARTICLE
Bounds on Fractional-Based Metric Dimension of Petersen Networks
Dalal Awadh Alrowaili1, Mohsin Raza2, Muhammad Javaid2,*
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 the 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 15 April 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 G
P(
n, 3), where
n ≥ 7. For
n ≥ 9. The limiting values of
LFMD for G
P(
n, 3) are also obtained as 1 (bounded) if
n approaches to infinity.
Keywords
Cite This Article
Alrowali, D. A., Raza, M., Javaid, M. (2023). Bounds on Fractional-Based Metric Dimension of Petersen Networks.
CMES-Computer Modeling in Engineering & Sciences, 135(3), 2697–2713. https://doi.org/10.32604/cmes.2023.023017