The COVID-19 outbreak has appeared as a matchless global threat against all humanity. Even the most developed countries have been shocked by the adversities of the COVID-19 pandemic affecting social life, especially human health. All over the world, researchers still have been studying to develop new medicines the combat outbreak. A topological index can be thought of as the conversion of a chemical structure to a real number. Topological indices are often used to provide information about the physicochemical properties and biological properties of molecules. Topological coindices are the numeric values, obtained by the complement graph of a molecular structure, which is used in Quantitative Structure Property/Activity Relationship (QSPR/QSAR) studies to evaluate the physicochemical and biological properties of compounds. In this study, we construct some new topological coindices and define the concept of $\mathit{CoNM}$-polynomial. Owing to these polynomials we pass the difficulty of calculating the topological coindices. The computing process is done for the molecular graph structure of fixed analogs of Lopinavir, Favipiravir and Ritonavir. Afterward, obtained values are evaluated in QSPR modeling via linear and quadratic regression analysis to examine some physicochemical properties of the analog medicines such as enthalpy of vaporization (E), flash point (FP), molar refractivity (MR), polarizability (P), surface tension (T), molar volume (MV).

Background: Chemical graph theory is a sub-branch of mathematical chemistry, assuming each atom of a molecule is a vertex and each bond between atoms as an edge. Objective: Owing to this theory, it is possible to avoid the difficulties of chemical analysis because many of the chemical properties of molecules can be determined and analyzed via topological indices. Due to these parameters, it is possible to determine the physicochemical properties, biological activities, environmental behaviours and spectral properties of molecules. Nowadays, studies on the zero divisor graph of Z_n via topological indices is a trending field in spectral graph theory. Methods: For a commutative ring R with identity, the prime ideal sum graph of R is a graph whose vertices are nonzero proper ideals of R and two distinctvertices I and J are adjacent if and only if I+J is a prime ideal of R. Results: In this study the forgotten topological index and Wiener index of the prime ideal sum graph of Z_n are calculated for n=p^α,pq,p^2 q,p^2 q^2,pqr,p^3 q,p^2 qr,pqrs where p,q,r and s are distinct primes and a Sage math code is developed for designing graph and computing the indices. Conclusion: In the light of this study, it is possible to handle the other topological descriptors for computing and developing new algorithms for next studies and to study some spectrum and graph energies of certain finite rings with respect to PIS-graph easily.