The spread of novel virus SARS‐CoV‐2, well known as COVID‐19 has become a major health issue currently which has turned up to a pandemic worldwide. The treatment recommendations are variable. Lack of appropriate medication has worsened the disease. On the basis of prior research, scientists are testing drugs based on medical therapies for SARS and MERS. Many drugs which include lopinavir, ritonavir and thalidomide are listed in the new recommendations. A topological index is a type of molecular descriptor that simply defines numerical values associated with the molecular structure of a compound that is effectively used in modeling many physicochemical properties in numerous quantitative structure–property/activity relationship (QSPR/QSAR) studies. In this study, several degree‐based and neighborhood degree sum‐based topological indices for several antiviral drugs were investigated by using a M ‐polynomial and neighborhood M ‐polynomial methods. In addition, a QSPR was established between the various topological indices and various physicochemical properties of these antiviral drugs along with remdesivir, chloroquine, hydroxychloroquine and theaflavin was performed in order to assess the efficacy of the calculated topological indices. The obtained results reveal that topological indices under study have strong correlation with the physicochemical characteristics of the potential antiviral drugs. A biological activity (pIC50) of these compounds were also investigated by using multiple linear regressions (MLR) analysis.

Quantitative structure–activity relationship (QSAR) represents quantitative correlation of chemical structural features called as molecular descriptors and pharmacological activity as response endpoints. Topological index is a molecular descriptor extensively used to study QSAR of pharmaceuticals to assess their molecular characteristics by numerical computation. Theoretical assessment of drug like molecules helps to expedite the drug design and discovery process by rationalizing the lead identification, lead optimization and understanding their mechanism of actions. Therefore, in this article, we have computed the general inverse sum indeg index, of Hyaluronic acid-curcumin conjugates by using molecular structure analysis and edge partitioning technique. Many standard topological indices are obtained as a special case of . We also proposed general inverse sum indeg polynomial of Hyaluronic acid-curcumin conjugates from which many well-known polynomials are deduced.

SARS-CoV-2 is a new strain of coronavirus family that has never been previously detected in humans. This has grown into a huge public health issue that has affected people all around the world. Presently, there is no specific antiviral treatment for COVID-19. To tackle the outbreak, a number of drugs are being explored or have been utilized based on past experience. A molecular descriptor (or topological index) is a numerical value that describes a compound’s molecular structure and has been successfully employed in many QSPR/QSAR investigations to represent several physicochemical attributes. In order to determine topological characteristics of graphs, coindices (topological) take nonadjacent pair of vertices into account. In this study, we introduced CoM-polynomial and numerous degree-based topological coindices for several antiviral medicines such as lopinavir, ritonavir remdesivir, hydroxychloroquine, chloroquine, theaflavin, thalidomide, and arbidol which were studied using the CoM-polynomial approach. In the QSPR model, the linear regression approach is used to analyze the relationships between physicochemical properties and topological coindices. The findings show that the topological coindices under investigation have a substantial relationship with the physicochemical properties of possible antiviral medicines in question. As a result, topological coindices may be effective tools for studying antiviral drugs in the future for QSPR analyses.

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The design of the quantitative structure-property/activity relationships for drug-related compounds using theoretical methods relies on appropriate molecular structure representations. The molecular structure of a compound comprises all the information required to determine its chemical, biological, and physical properties. These properties can be assessed by employing a graph theoretical descriptor tool widely known as topological indices. Generalization of descriptors may reduce not only the number of molecular graph-based descriptors but also improve existing results and provide a better correlation to several molecular properties. Recently introduced ve-degree and ev-degree topological indices have been successfully employed for development of models for the prediction of various biological activities/properties. In this article, we propose the general ve-inverse sum indeg index ISI α , β ve G and general ve-Zagreb index M α ve G of graph G and compute ISI α , β ve G , M α ve G , and M α ev G (general ev-degree index) of hyaluronic acid-curcumin/paclitaxel conjugates, renowned for its potential anti-inflammatory, antioxidant, and anticancer properties, by using molecular structure analysis and edge partitioning technique. Several ve-degree- and ev-degree-based topological indices are obtained as a special case of ISI α , β ve G , M α ve G , and M α ev G . Furthermore, QSPR analysis of ISI α , β ve G , M α ve G , and M α ev G for particular values of α and β is performed, which reveals their predicting power. These results allow researchers to better understand the physicochemical properties and pharmacological characteristics of these conjugates.

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Chemical descriptors are numeric numbers that capture the whole graph structure and comprise a basic chemical structure. As a topological descriptor, it correlates with certain physical aspects in addition to its chemical representation of underlying chemical substances. In the modelling and design of any chemical network, the graph is important. A number of chemical indices have been developed in theoretical chemistry, including the Wiener index, the Randić index, and many others. In this paper, we look at the benzenoid networks and calculate the exact topological indices based on the degrees of the end vertices.

Using Wilson's GF matrix method as modified by Higgs for an infinite system, we report normal modes and their dispersion for polyoxymethylene using the Urey-Bradley force field. Heat capacity has been evaluated as a function of temperature from dispersion curves via density-of-states. The results obtained agree well with the experimental data reported in the literature.