Topological indices serve as a crucial component in chemical graph theory linked with some molecular structure. The First and Second Zagreb Indices are one among the earliest and extensively explored molecular descriptors. The study on equitable zagreb indices have been initiated earlier by Akram Alqesmah, Anwar Alwardi and R. Rangarajan based on the equitable degree of the vertices. In this paper, we introduce the first and second equitable and non-equitable zagreb polynomials and compute the exact values of the respective equitable and non-equitable zagreb indices for polycyclic aromatic hydrocarbons. We have also utilised certain formulations for the determination of the corresponding relative equitable and non-equitable zagreb indices of the chemical graph. Further, QSPR analysis is carried out for the topological indices with regard to the physico-chemical properties of the polycyclic hydrocarbon molecules.

The network systems and graphical analysis through the study ofstructural characteristics is a vast field of growing importance inresearch. Topological indices have a significant and crucial role inthe study of structure–property relationships. In this paper, weexamine constructional transformed networks constructed by unique vertex-edge incidence and mutual adjacency associations. Expres-sions for the first and second hyper Zagreb indices and co-indices of these transformed networks and their complements are obtained. MSC Classification: 05C09 , 05C90 , 05C92