This paper describes a new technique to compute topological indices of donut benzenoids and Kekulenes with applications to drugs by dissecting the original topological network into smaller strength-weighted quotient graphs relative to the transitive closure of the Djokovi –Winkler relation. We have applied this technique to a series of donut benzenoid graphs obtained by circumcising at least two internal hexagons from parent benzenoid graphs. Such donut coronoid graph finds significant applications in emerging chemical materials of importance to synthetic organic chemistry and drug industry. It comprised of donut coronoid structures such as Kekulenes and related circumscribed structures where a number of graph-theoretical based techniques, such as resonance theory and Clar’s sextets. In this work, we have computed a number of topological indices of these donut coronoid systems such as the Wiener index, variants of Szeged, Schultz and Gutman indices.

The physicochemical characteristics of polycyclic aromatic compounds critical to environmental modelling such as octanol partition coefficients, solubility, lipophilicity, polarity and several equilibrium constants are functions of their underlying molecular structures, prompting the development of mathematical models to predict such characteristics for which experimental results are difficult to obtain. We propose twelve novel descriptors derived from geometric, harmonic and Zagreb degree-based descriptors and then test the effectiveness of these descriptors on a data set consisting of 55 benzenoid hydrocarbons of environmental importance. Our computations show that the proposed descriptors have a good linear correlation and predictive power when compared to the degree and distance type descriptors. We have also derived the QSPR expressions for four properties of a large series of polycyclic aromatics arising from circumscribing coronenes and show that a scaling factor can be deduced to derive physicochemical properties of such series up to 2D graphene sheets.

The entire world is struggling to control the spread of coronavirus (COVID‐19) as there are no proper drugs for treating the disease. Under clinical trials, some of the repurposed antiviral drugs have been applied to COVID‐19 patients and reported the efficacy of the drugs with the diverse inferences. Molecular topology has been developed in recent years as an influential approach for drug design and discovery in which molecules that are structurally related show similar pharmacological properties. It permits a purely mathematical description of the molecular structure so that in the development of identification of new drugs can be found through adequate topological indices. In this paper, we study the structural properties of the several antiviral drugs such as chloroquine, hydroxychloroquine, lopinavir, ritonavir, remdesivir, theaflavin, nafamostat, camostat, umifenovir and bevacizumab by considering the distance and bond measures of chemical compounds. Our quantitative values of the topological indices are extremely useful in the recent development of designing new drugs for COVID‐19.