Degree-based topological indices and total π-electron energies of some benzenoid hydrocarbons: correlations of strain energies and bulk modulus with such indices

Abstract Degree-based and neighbourhood degree-sum-based (or hybrid degree-based) topological indices (TIs) for some benzenoid hydrocarbons viz. linear polyacences, methylene substituated linear polyacences, cyclacenes, linear poly ( p -phenylenes), methylene substituated linear poly ( p -phenylenes), and cylindrical poly ( p -phenylenes) with r hexagonal rings are expressed as linear functions of r . For a given system the variation of degree-based Randić and harmonic indices or that of their hybrid indices with r is quite similar while that differs with their corresponding hybrid degree-based indices. The geometric-arithmetic index is the only one among the indices for a given system which is found to remain unaffected under consideration of neighbourhood effect. Total π -electron energies for such systems have also been derived as linear functions of r from their respective eigenspectra. Although all such TIs discussed here have good linear correlations with the total π -electron energies of the respective systems but among them the geometric-arithmetic degree-based and hybrid degree-based TIs are the best to correlate total π -electron energies for such systems. The inverses of the degree-based and hybrid degree-based TIs of cyclacenes and cylindrical poly ( p -phenylenes) are found to correlate excellently well with their strain energies. The good linear correlations are also found with the inverses of the TIs of linear poly ( p -phenylenes) with 2–6 hexagonal rings and their respective bulk modulus.