In recent times, machine learning being an exciting area, has attracted a lot of studies for its ability to foresee complex chemical and biological properties of chemical compounds used in drug design. This article proposes a machine-learning based quantitative structure-property relationship(QSPR) model for benzenoid hydrocarbons and their physical properties through eigenvalues-based graphical indices. Benzenoid hydrocarbons play a crucial role in drug design and pharmaceutical chemistry due to their stability, aromaticity, and ability to participate in various biological interactions. To validate the results, machine learning technique is applied to predict the properties using various graphical indices. Further, to rank the best hydrocarbon MCDM technique namely SAW is adopted. From the analysis, it is obvious that the best predictive graphical index is Laplacian energy for the property polarizability and the best hydrocarbon is Dibenzo[a,h]pyrene.