For a long time, the structure and characteristics of benzene and other
arenes have piqued researchers curiosity in quantum chemistry. The
structural features of polycyclic aromatic compounds, like the
fundamental molecular topology, have a strong influence on their
chemical and biological properties. Quantitative structure-activity and
property relationship (QSAR/QSPR) techniques for predicting
characteristics of polycyclic aromatic compounds (PAC) and related
graphs from chemical structures have been developed in this approach. To
obtain degree-based topological indices, we have many polynomials. The
neighbourhood M-polynomial is one of these polynomials, which is used to
produce a number of topological indices based on neighborhood degree
sum. In this study, we offer the exact analytical expressions of
neighborhood M-polynomial and their corresponding topological indices
for supercoronene (SC), cove-hexabenzocoronene (cHBC), and
triangular-shaped discotic graphene (TDG) with hexabenzocorenene (HBC)
as the base molecule. The findings could help with the development of
physicochemical characteristic prediction.