Clar covering polynomials of polycyclic aromatic hydrocarbons

Peirong Li; Hong Bian; Haizheng Yu; Yan Dou; Peirong Li; Hong Bian; Haizheng Yu; Yan Dou

doi:10.3934/math.2024653

AIMS Mathematics

2024, Volume 9, Issue 5: 13385-13409. doi: 10.3934/math.2024653

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Research article

Clar covering polynomials of polycyclic aromatic hydrocarbons

1.
School of Mathematical Sciences, Xinjiang Normal University, No. 102, Xinyi Rd. Urumuqi 830054, China
2.
College of Mathematics and System Sciences, Xinjiang University, No. 666, Shengli Rd. Urumuqi 830046, China
3.
College of Education Science, Xinjiang Normal University, No. 102, Xinyi Rd. Urumuqi 830054, China

Received: 05 February 2024 Revised: 22 March 2024 Accepted: 01 April 2024 Published: 11 April 2024
MSC : 05C85, 05C92

Polycyclic aromatic hydrocarbon (PAH) is a compound composed of carbon and hydrogen atoms. Chemically, large PAHs contain at least two benzene rings and exist in a linear, cluster, or angular arrangement. Hexagonal systems are a typical class of PAHs. The Clar covering polynomial of hexagonal systems contains many important topological properties of condensed aromatic hydrocarbons, such as Kekulé number, Clar number, first Herndon number, which is an important theoretical quantity for predicting the aromatic stability of PAH conjugation systems, and so on. In this paper, we first obtained some recursive formulae for the Clar covering polynomials of double hexagonal chains and proposed a Matlab algorithm to compute the Clar covering polynomial of any double hexagonal chain. Moreover, we presented the characterization of extremal double hexagonal chains with maximum and minimum Clar covering polynomials in all double hexagonal chains with fixed $ s $ naphthalenes.
- polycyclic aromatic hydrocarbons,
- hexagonal system,
- Clar covering polynomial,
- double hexagonal chain,
- peri-condensed hexagonal system
Citation: Peirong Li, Hong Bian, Haizheng Yu, Yan Dou. Clar covering polynomials of polycyclic aromatic hydrocarbons[J]. AIMS Mathematics, 2024, 9(5): 13385-13409. doi: 10.3934/math.2024653

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Abstract

Polycyclic aromatic hydrocarbon (PAH) is a compound composed of carbon and hydrogen atoms. Chemically, large PAHs contain at least two benzene rings and exist in a linear, cluster, or angular arrangement. Hexagonal systems are a typical class of PAHs. The Clar covering polynomial of hexagonal systems contains many important topological properties of condensed aromatic hydrocarbons, such as Kekulé number, Clar number, first Herndon number, which is an important theoretical quantity for predicting the aromatic stability of PAH conjugation systems, and so on. In this paper, we first obtained some recursive formulae for the Clar covering polynomials of double hexagonal chains and proposed a Matlab algorithm to compute the Clar covering polynomial of any double hexagonal chain. Moreover, we presented the characterization of extremal double hexagonal chains with maximum and minimum Clar covering polynomials in all double hexagonal chains with fixed $ s $ naphthalenes.

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