Extremal values of VDB topological indices over F-benzenoids with equal number of edges

Fengwei Li; Qingfang Ye; Juan Rada; Fengwei Li; Qingfang Ye; Juan Rada

doi:10.3934/mbe.2023240

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 3: 5169-5193. doi: 10.3934/mbe.2023240

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Extremal values of VDB topological indices over F-benzenoids with equal number of edges

1.
College of Basic Science, Ningbo University of Finance & Economics, Ningbo 315175, China
2.
Instituto de Matemáticas, Universidad de Antioquia, Medellín, Colombia

Academic Editor: José M. Rodríguez

Received: 12 November 2022 Revised: 20 December 2022 Accepted: 26 December 2022 Published: 09 January 2023

The utilization of molecular structure topological indices is currently a standing operating procedure in the structure-property relations research, especially in QSPR/QSAR study. In the past several year, generous molecular topological indices related to some chemical and physical properties of chemical compounds were put forward. Among these topological indices, the VDB topological indices rely only on the vertex degree of chemical molecular graphs. The VDB topological index of an $ n $-order graph $ G $ is defined as

$ TI(G) = \sum\limits_{1\leq i\leq j\leq n-1}m_{ij}\psi_{ij}, $

where $ \{\psi_{ij}\} $ is a set of real numbers, $ m_{ij} $ is the quantity of edges linking an $ i $-vertex and another $ j $-vertex. Numerous famous topological indices are special circumstance of this expression. f-benzenoids are a kind of polycyclic aromatic hydrocarbons, present in large amounts in coal tar. Studying the properties of f-benzenoids via topological indices is a worthy task. In this work the extremum $ TI $ of f-benzenoids with given number of edges were determined. The main idea is to construct f-benzenoids with maximal number of inlets and simultaneously minimal number of hexagons in $ \Gamma_{m} $, where $ \Gamma_{m} $ is the collection of f-benzenoids with exactly $ m $ $ (m\geq19) $ edges. As an application of this result, we give a unified approach of VDB topological indices to predict distinct chemical and physical properties such as the boiling point, $ \pi $-electrom energy, molecular weight and vapour pressure etc. of f-benzenoids with fixed number of edges.
- VDB topological index,
- inlet,
- f-spiral benzenoid,
- f-linear chain,
- f-benzenoid
Citation: Fengwei Li, Qingfang Ye, Juan Rada. Extremal values of VDB topological indices over F-benzenoids with equal number of edges[J]. Mathematical Biosciences and Engineering, 2023, 20(3): 5169-5193. doi: 10.3934/mbe.2023240

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Abstract

The utilization of molecular structure topological indices is currently a standing operating procedure in the structure-property relations research, especially in QSPR/QSAR study. In the past several year, generous molecular topological indices related to some chemical and physical properties of chemical compounds were put forward. Among these topological indices, the VDB topological indices rely only on the vertex degree of chemical molecular graphs. The VDB topological index of an $ n $-order graph $ G $ is defined as

$ TI(G) = \sum\limits_{1\leq i\leq j\leq n-1}m_{ij}\psi_{ij}, $

where $ \{\psi_{ij}\} $ is a set of real numbers, $ m_{ij} $ is the quantity of edges linking an $ i $-vertex and another $ j $-vertex. Numerous famous topological indices are special circumstance of this expression. f-benzenoids are a kind of polycyclic aromatic hydrocarbons, present in large amounts in coal tar. Studying the properties of f-benzenoids via topological indices is a worthy task. In this work the extremum $ TI $ of f-benzenoids with given number of edges were determined. The main idea is to construct f-benzenoids with maximal number of inlets and simultaneously minimal number of hexagons in $ \Gamma_{m} $, where $ \Gamma_{m} $ is the collection of f-benzenoids with exactly $ m $ $ (m\geq19) $ edges. As an application of this result, we give a unified approach of VDB topological indices to predict distinct chemical and physical properties such as the boiling point, $ \pi $-electrom energy, molecular weight and vapour pressure etc. of f-benzenoids with fixed number of edges.

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