Fault-tolerance in metric dimension of boron nanotubes lattices

Zafar Hussain; Muhammad Mobeen Munir

doi:10.3389/fncom.2022.1023585

Fault-tolerance in metric dimension of boron nanotubes lattices

Front Comput Neurosci. 2023 Jan 25:16:1023585. doi: 10.3389/fncom.2022.1023585. eCollection 2022.

Authors

Zafar Hussain¹, Muhammad Mobeen Munir²

Affiliations

¹ Department of Mathematics and Statistics, The University of Lahore, Lahore, Pakistan.
² Department of Mathematics, University of the Punjab, Lahore, Pakistan.

Abstract

The concept of resolving set and metric basis has been very successful because of multi-purpose applications both in computer and mathematical sciences. A system in which failure of any single unit, another chain of units not containing the faulty unit can replace the originally used chain is called a fault-tolerant self-stable system. Recent research studies reveal that the problem of finding metric dimension is NP-hard for general graphs and the problem of computing the exact values of fault-tolerant metric dimension seems to be even harder although some bounds can be computed rather easily. In this article, we compute closed formulas for the fault-tolerant metric dimension of lattices of two types of boron nanotubes, namely triangular and alpha boron. These lattices are formed by cutting the tubes vertically. We conclude that both tubes have constant fault tolerance metric dimension 4.

Keywords: 2-d lattices; boron tubes; fault-tolerant metric dimension; metric basis; metric dimension; resolving set.