Spectral Graph Theory is the interface that connects the graphs and the matrices associated with them. Chemistry is the branch of science which has benefitted the most out of this interaction as the information-theoretic matrices of the molecular graphs offer immensely useful molecular descriptors. Graph energy and topological indices are chemistry-initiated directions of research in mathematics. In this paper, we compute the characteristic polynomial of Circum-coronene(n) series of benzenoid graphs, 1 ≤ n ≤ 3 and few degree-based topological indices of Circum-polyacenes(m, n), Circum-pyrene(n) and Circum-trizene(n). Also, the graph invariants namely energy, spectral radius, Wiener index, first Zagreb index, modified first Zagreb index, second Zagreb index and modified second Zagreb index have been computed for few proposed drugs against COVID-19, their extensions and coronoid networks. We have also verified our results using MATLAB programs.