Reciprocal Atom-bond connectivity and Fourth Atom-bond connectivity indices for Polyphenylene structure of molecules

Polyphenylene is a class of polycyclic aromatic compounds that has varied applications in biochemistry and biology. A numerical measure that defines the characteristics of a chemical structure is called topological index. In chemical graph theory, Estrada et al. proposed the degree-based topological indices known as Atom-bond connectivity index (𝐴𝐵𝐶) [4]. A new version of 𝐴𝐵𝐶 index is Fourth Atom-bond connectivity index (𝐴𝐵𝐶4 ) proposed by M. Ghorbani et al. [6]. A valuable predictive index in the study of the heat of formation of alkanes, the strain energy of cycloalkanes is 𝐴𝐵𝐶 index. Based on this, numerous articles were reported. In this study, novel indices, Reciprocal Atom-bond Connectivity (𝑅𝐴𝐵𝐶) and Reciprocal Fourth Atom-bond connectivity(𝑅𝐴𝐵𝐶4) indices were proposed and a comparative study of correlation with properties of octane isomers were given. It was observed that these indices showed good correlation for physico chemical properties of octane isomers. Subsequently, Reciprocal Atom-bond connectivity and Reciprocal Fourth Atom-bond connectivity indices for Polyphenylene structure of molecules were computed.