Clar covering polynomials of polycyclic aromatic hydrocarbons

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.