The ongoing COVID-19 pandemic continues to pose significant challenges worldwide, despite widespread vaccination. Researchers are actively exploring antiviral treatments to assess their efficacy against emerging virus variants. The aim of the study is to employ M-polynomial, neighborhood M-polynomial approach and QSPR/QSAR analysis to evaluate specific antiviral drugs including Lopinavir, Ritonavir, Arbidol, Thalidomide, Chloroquine, Hydroxychloroquine, Theaflavin and Remdesivir. Utilizing degree-based and neighborhood degree sum-based topological indices on molecular multigraphs reveals insights into the physicochemical properties of these drugs, such as polar surface area, polarizability, surface tension, boiling point, enthalpy of vaporization, flash point, molar refraction and molar volume are crucial in predicting their efficacy against viruses. These properties influence the solubility, permeability, and bio availability of the drugs, which in turn affect their ability to interact with viral targets and inhibit viral replication. In QSPR analysis, molecular multigraphs yield notable correlation coefficients exceeding those from simple graphs: molar refraction (MR) (0.9860), polarizability (P) (0.9861), surface tension (ST) (0.6086), molar volume (MV) (0.9353) using degree-based indices, and flash point (FP) (0.9781), surface tension (ST) (0.7841) using neighborhood degree sum-based indices. QSAR models, constructed through multiple linear regressions (MLR) with a backward elimination approach at a significance level of 0.05, exhibit promising predictive capabilities highlighting the significance of the biological activity $$IC_{50}$$I C 50 (Half maximal inhibitory concentration). Notably, the alignment of predicted and observed values for Remdesivir’s with obs $${pIC_{50} = 6.01}$$p I C 50 = 6.01 ,pred $${pIC_{50} = 6.01}$$p I C 50 = 6.01 ( $$pIC_{50}$$p I C 50 represents the negative logarithm of $$IC_{50}$$I C 50 ) underscores the accuracy of multigraph-based QSAR analysis. The primary objective is to showcase the valuable contribution of multigraphs to QSPR and QSAR analyses, offering crucial insights into molecular structures and antiviral properties. The integration of physicochemical applications enhances our understanding of factors influencing antiviral drug efficacy, essential for combating emerging viral strains effectively.

Fractional derivatives are notable for various reasons, including the fact that they have properties of non-fractional derivatives, such as making constant derivatives null. Furthermore, nowadays, ...

In this study, we introduce a novel valency-based index, the neighborhood face index (NFI), designed to characterize the structural attributes of benzenoid hydrocarbons. To assess the practical applicability of NFI, we conducted a linear regression analysis utilizing numerous physiochemical properties associated with benzenoid hydrocarbons. Remarkably, the results revealed an extraordinary correlation exceeding 0.9991 between NFI and these properties, underscoring the robust predictive capability of the index. The NFI, identified as the best-performing descriptor, is subsequently investigated within certain infinite families of carbon nanotubes. This analysis demonstrates the index’s exceptional predictive accuracy, suggesting its potential as a versatile tool for characterizing and predicting properties across diverse molecular structures, particularly in the context of carbon nanotubes.

Graph theory (GT) is a mathematical field that involves the study of graphs or diagrams that contain points and lines to represent the representation of mathematical truth in a diagrammatic format. From simple graphs, complex network architectures can be built using graph operations. Topological indices (TI) are graph invariants that correlate the physicochemical and interesting properties of different graphs. TI deal with many properties of molecular structure as well. It is important to compute the TI of complex structures. The corona product (CP) of two graphs and gives us a new graph obtained by taking one copy of and copies of and joining the th vertex of to every vertex in the th copy of . In this paper, based on various CP graphs composed of paths, cycles, and complete graphs, the geometric index (GA) and atom bond connectivity (ABC) index are investigated. Particularly, we discussed the corona products , , , , and and GA and ABC index. Moreover, a few molecular graphs and physicochemical features may be predicted by considering relevant mathematical findings supported by proofs.

This paper describes a generalized Diophantine fuzzy sets, which can be seen as a generalization of both Diophantine fuzzy sets and Pythagorean fuzzy sets. We define the basic properties of generalized Diophantine fuzzy set, as well as their relationships and distances. We compare Diophantine fuzzy sets with other Diophantine Pythagorean fuzzy sets to demonstrate their importance in the literature. We introduce new operators including necessity, possibility, accuracy function and score function. Furthermore, we discuss the new distance between normalized Euclidean distance and normalized Hamming distance. For a generalized Diophantine fuzzy relation, image and inverse image functions are defined. Numerous real-world applications can be found for the prevalent ideas of intuitionistic fuzzy sets, Pythagorean fuzzy sets, Diophantine fuzzy sets and q-rung orthopair fuzzy sets. Regretfully, these theories about the membership and non-membership grades have their own limits. We provide a new idea the generalized Diophantine fuzzy set that eliminates these limitations by including reference parameters. Compared to other kinds of fuzzy sets, there are more applications for generalized Diophantine fuzzy sets. We offer practical examples that show how different enhanced distances might be used in everyday situations. Additionally, to demonstrate the effectiveness of the suggested approach, flowchart based multi-criteria decision-making is provided and used to a numerical example. The outcomes are assessed for various parameter values. Furthermore, a comparative analysis developed to demonstrate the superiority of the suggested technique over current methodologies.

In this study, an extensive examination of topological parameters derived from molecular structures is conducted, with a specific focus on the Randic index, Geometric Arithmetic (GA) index, and Atom Bond Connectivity (ABC) index. These indices are applied to concealed non-Kekulean benzenoids and subdivided networks within line graphs. The investigation reveals patterns and relationships that were previously unexplored, shedding light on the structural intricacies of chemical compounds. The utility of graph theory as an effective tool for modeling and designing interconnection devices within the realm of chemical research is underscored. Such an approach not only advances the field of mathematical chemistry but also enriches understanding of the manipulation of chemical structures for extensive scientific applications. This analysis contributes to the body of knowledge by highlighting the relevance of these indices in unveiling complex molecular topologies and their potential implications for theoretical and applied chemistry.