On Hosoya polynomial and subsequent indices of pent–heptagonal carbon nanosheets

Abstract

The pent–heptagonal carbon nanosheets (CNSs) admit significant industrial applications. We shall compute the distance-based Hosoya polynomial of CNSs including [Formula: see text] and [Formula: see text]. The first-, second- and third-order derivatives of Hosoya polynomial, respectively, lead to the Wiener, hyper-Wiener and Tratch–Stankevitch–Zefirov (TSZ) indices which are the distance-based topological indices. These indices have many physical applications and can be correlated to physio-chemical properties of chemical structures. Results exhibit that despite the fact that both sheets have the same chemical formula, they have different Hosoya polynomials and related distance-based topological indices, resulting in distinct quantitative structure–property relation (QSPR) and quantitative structure–activity relation (QSAR) due to configuration differences.