M-polynomials and topological indices of linear chains of benzene, napthalene and anthracene

Cheng-Peng Li; Cheng Zhonglin; Mobeen Munir; Kalsoom Yasmin; Jia-bao Liu; Cheng-Peng Li; Cheng Zhonglin; Mobeen Munir; Kalsoom Yasmin; Jia-bao Liu

doi:10.3934/mbe.2020127

Mathematical Biosciences and Engineering

2020, Volume 17, Issue 3: 2384-2398. doi: 10.3934/mbe.2020127

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Research article Special Issues

M-polynomials and topological indices of linear chains of benzene, napthalene and anthracene

1.
Techanical and Electrical Engineering Department, Anqing Vocational and Technical College, Anqing 246003, P.R. China
2.
Teaching Department of Public Basic Course, Anhui International University, Hefei 231201, China
3.
Department of Mathematics, Division of Science and Technology, University of Education, Lahore-54590, Pakistan
4.
School of Mathematics, Southeast University, Nanjing 210096, China

Received: 15 October 2019 Accepted: 31 December 2019 Published: 14 February 2020

The universality of M-polynomial paves way towards establishing closed forms of many leading degree-based topological indices as it is done by Hosoya polynomial for distance-based indices. The study of topological indices is recently one of the most active research areas in chemical graph theory. The aim of this paper is to establish closed formulas for M-polynomials of Linear chains of benzene, napthalene, and anthracene graphs. From this polynomial we also compute as many as nine degree-based topological indices for these three chains. Our results will potentially play an important role in pharmacy, drug design, and many other applied areas of molecular sciences.
- M-polynomial,
- degree-based index,
- linear chain of benzene,
- napthalene,
- anthracene
Citation: Cheng-Peng Li, Cheng Zhonglin, Mobeen Munir, Kalsoom Yasmin, Jia-bao Liu. M-polynomials and topological indices of linear chains of benzene, napthalene and anthracene[J]. Mathematical Biosciences and Engineering, 2020, 17(3): 2384-2398. doi: 10.3934/mbe.2020127

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Abstract

The universality of M-polynomial paves way towards establishing closed forms of many leading degree-based topological indices as it is done by Hosoya polynomial for distance-based indices. The study of topological indices is recently one of the most active research areas in chemical graph theory. The aim of this paper is to establish closed formulas for M-polynomials of Linear chains of benzene, napthalene, and anthracene graphs. From this polynomial we also compute as many as nine degree-based topological indices for these three chains. Our results will potentially play an important role in pharmacy, drug design, and many other applied areas of molecular sciences.

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