Local Fractional Strong Metric Dimension of Certain Rotationally Symmetric Planer Networks

Agha Kashif,Abdulaziz Mohammed Alanazi,Faiza Jamil,Zaid Bassfar,Sohail Zafar

doi:10.1109/access.2021.3131311

Agha Kashif, Abdulaziz Mohammed Alanazi

Open Access

https://doi.org/10.1109/access.2021.3131311

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Abstract

Fractional versions of metric based networks invariants widen the scope of application in fields of intelligent systems, computer science and chemistry including, robot navigation, sensor networking, linear optimization problems, scheduling, assignment, operation research problems, image processing and drug discovery. It plays vital role in the study to check structural properties of the networks such as complexity, modularity and accessibility. Rotationally symmetric and planer networks have key importance in the fields of robot navigation, networking, telecommunication and chemistry due the structure of these networks which help in optimal rate of data transfer and minimize the time taken and resources used. In this paper we introduce a combinatorial technique to compute local fractional strong metric dimension (LFSMD) of networks. The technique is further used to compute LFSMD of certain rotationally symmetric planer networks.

Highlights

A days, human labour is being replaced by robotics and machineries due to computerization and mechanization in every field
The concepts of resolving sets and metric dimension were introduced by Slater [23] in 1975 and independently by Harary and Melter [9] later in 1976
Arumugam and Mathew [2] introduced the concept of resolving neighbourhoods to define fractional metric dimension in 2012

Summary

INTRODUCTION

Human labour is being replaced by robotics and machineries due to computerization and mechanization in every field These advancements reduce the need of labour but these essential in producing the required output to meet the demand at a competitive cost with optimization of the resources. In 2013, Kang and Yi [11] introduced fractional strong metric dimension and computed it for some important classes of finite simple graphs. We introduce localized version of fractional strong metric dimension and determine local fractional strong metric dimension of rotationally symmetric and planer networks.

PRELIMINARIES

LOCAL STRONG RESOLVING NEIGHBOURHOODS

LOCAL FRACTIONAL STRONG METRIC DIMENSION

APPLICATION

CONCLUSION