Partition dimension of COVID antiviral drug structures

Ali Al Khabyah; Muhammad Kamran Jamil; Ali N. A. Koam; Aisha Javed; Muhammad Azeem; Ali Al Khabyah; Muhammad Kamran Jamil; Ali N. A. Koam; Aisha Javed; Muhammad Azeem

doi:10.3934/mbe.2022471

Mathematical Biosciences and Engineering

2022, Volume 19, Issue 10: 10078-10095. doi: 10.3934/mbe.2022471

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Research article

Partition dimension of COVID antiviral drug structures

1.
Department of Mathematics, College of Science, Jazan University, New Campus, Jazan 2097, Saudi Arabia
2.
Department of Mathematics, Riphah Institute of Computing and Applied Sciences, Riphah International University Lahore, Pakistan
3.
Abdus Salam School of Mathematical Sciences, Government College University, Lahore, Pakistan

Received: 13 April 2022 Revised: 09 June 2022 Accepted: 10 June 2022 Published: 15 July 2022

In November 2019, there was the first case of COVID-19 (Coronavirus) recorded, and up to 3$ ^{rd }$ of April 2020, 1,116,643 confirmed positive cases, and around 59,158 dying were recorded. Novel antiviral structures of the SARS-COV-2 virus is discussed in terms of the metric basis of their molecular graph. These structures are named arbidol, chloroquine, hydroxy-chloroquine, thalidomide, and theaflavin. Partition dimension or partition metric basis is a concept in which the whole vertex set of a structure is uniquely identified by developing proper subsets of the entire vertex set and named as partition resolving set. By this concept of vertex-metric resolvability of COVID-19 antiviral drug structures are uniquely identified and helps to study the structural properties of structure.
- COVID antiviral drug structure,
- vertex metric dimension,
- partition dimension,
- partition locating number,
- partition locating set
Citation: Ali Al Khabyah, Muhammad Kamran Jamil, Ali N. A. Koam, Aisha Javed, Muhammad Azeem. Partition dimension of COVID antiviral drug structures[J]. Mathematical Biosciences and Engineering, 2022, 19(10): 10078-10095. doi: 10.3934/mbe.2022471

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Abstract

In November 2019, there was the first case of COVID-19 (Coronavirus) recorded, and up to 3$ ^{rd }$ of April 2020, 1,116,643 confirmed positive cases, and around 59,158 dying were recorded. Novel antiviral structures of the SARS-COV-2 virus is discussed in terms of the metric basis of their molecular graph. These structures are named arbidol, chloroquine, hydroxy-chloroquine, thalidomide, and theaflavin. Partition dimension or partition metric basis is a concept in which the whole vertex set of a structure is uniquely identified by developing proper subsets of the entire vertex set and named as partition resolving set. By this concept of vertex-metric resolvability of COVID-19 antiviral drug structures are uniquely identified and helps to study the structural properties of structure.

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