Extremal values of the first reformulated Zagreb index for molecular trees with application to octane isomers

Shabana Anwar; Muhammad Kamran Jamil; Amal S. Alali; Mehwish Zegham; Aisha Javed; Shabana Anwar; Muhammad Kamran Jamil; Amal S. Alali; Mehwish Zegham; Aisha Javed

doi:10.3934/math.2024017

AIMS Mathematics

2024, Volume 9, Issue 1: 289-301. doi: 10.3934/math.2024017

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Extremal values of the first reformulated Zagreb index for molecular trees with application to octane isomers

1.
Department of Mathematics, Riphah International University, Lahore, Pakistan
2.
Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
3.
Abdus Salam School of Mathematical Sciences, Government College University, Lahore, Pakistan

Received: 15 September 2023 Revised: 08 November 2023 Accepted: 14 November 2023 Published: 27 November 2023
MSC : 05C92, 05C90

A connected acyclic graph in which the degree of every vertex is at most four is called a molecular tree. A number associated with a molecular tree that can help to approximate the physical or chemical properties of the corresponding molecule is called a topological index. It is of great importance to investigate the relation between the structure and the thermodynamic properties of those molecules. In this paper, we investigated the extreme value of the first reformulated Zagreb index with a given order and degree of a graph. Further, we investigated the molecular trees that attain the maximum and minimum values. As an application, we presented the regression models to predict the acentric factor and entropy of octane isomers. Our extremal graphs give the minimum and the maximum acentric factor and entropy, which satisfied the experimental values.
- molecular tree,
- first reformulated Zagreb index,
- extremal trees,
- entropy,
- isomers
Citation: Shabana Anwar, Muhammad Kamran Jamil, Amal S. Alali, Mehwish Zegham, Aisha Javed. Extremal values of the first reformulated Zagreb index for molecular trees with application to octane isomers[J]. AIMS Mathematics, 2024, 9(1): 289-301. doi: 10.3934/math.2024017

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Abstract

A connected acyclic graph in which the degree of every vertex is at most four is called a molecular tree. A number associated with a molecular tree that can help to approximate the physical or chemical properties of the corresponding molecule is called a topological index. It is of great importance to investigate the relation between the structure and the thermodynamic properties of those molecules. In this paper, we investigated the extreme value of the first reformulated Zagreb index with a given order and degree of a graph. Further, we investigated the molecular trees that attain the maximum and minimum values. As an application, we presented the regression models to predict the acentric factor and entropy of octane isomers. Our extremal graphs give the minimum and the maximum acentric factor and entropy, which satisfied the experimental values.

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