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.

Topological indices (TIs) are numerical tools widely applied in chemometrics, biomedicine, and bioinformatics for predicting diverse physicochemical attributes and biological activities within molecular structures. Despite their significance, the challenges in deriving TIs necessitate novel approaches. This study addresses the limitations of conventional methods in dealing with dynamic molecular structures, focusing on the neighborhood M-polynomial (NM-polynomial), a pivotal polynomial for calculating degree-based TIs. Current literature acknowledges these polynomials but overlooks their limited adaptability to intricate biopolymer relationships. Our research advances by computing degree-based and neighborhood degree-based indices for prominent biopolymers, including polysaccharides, poly--glutamic acid, and poly-L-lysine. Through innovative utilization of the NM-polynomial and the M-polynomial, we establish a fresh perspective on molecular structure and topological indices. Moreover, we present diverse graph representations highlighting the nuanced correlations between indices and structural parameters. By systematically investigating these indices and their underlying polynomials, our work contributes to predictive modelling in various fields. This exploration sheds light on intricate biochemical systems, offering insights into applications encompassing medicine, the food industry, and wastewater treatment. This research deepens our understanding of complex molecular interactions and paves the way for enhanced applications in diverse industries.

يعد تحليل العلاقات الكمية بين البنية والممتلكات/النشاط (QSPR/QSAR) أمرًا بالغ الأهمية لفهم خصائص المركبات المرتبطة بالمخدرات، خاصة في علاج مرض الزهايمر. في هذه الدراسة، هدفنا هو استخدام أساليب مبتكرة بما في ذلك استخدام المؤشرات الطوبولوجية -درجة و- درجة ، المستمدة من نظرية الرسم البياني، لتقييم الخصائص والخصائص الفيزيائية والكيميائية لخمسة أدوية لمرض الزهايمر: تاكرين، دونيبيزيل، ريفيستيجمين، جالانتامين و والهوبرزين أ . تقدم هذه المؤشرات الطوبولوجية طريقة جديدة لالتقاط المعلومات الهيكلية الجزيئية الأساسية، مما يقلل من عدد الواصفات مع تعزيز ارتباطها بالخصائص الجزيئية المتنوعة. ومن خلال الحسابات الشاملة لهذه المؤشرات، هدفنا هو توضيح الخصائص الجزيئية المعقدة لأدوية مرض الزهايمر. علاوة على ذلك، أجرينا تحليلات QSPR وQSAR لربط المؤشرات الطوبولوجية المحسوبة بالخصائص الفيزيائية والكيميائية المختلفة للأدوية. في حين أن الأساليب المبتكرة المستخدمة في دراستنا توفر رؤى قيمة. لا تساهم النتائج التي توصلنا إليها في تعزيز فهمنا لخصائص أدوية مرض الزهايمر فحسب، بل تحمل أيضًا آثارًا على تطوير الأدوية وتحسينها في...

Topological indices are numerical descriptors that aid in the prediction of chemical molecules’ physiochemical properties and biological actions. It is often helpful to forecast numerous physiochemical attributes and biological actions of molecules in chemometrics, bioinformatics, and biomedicine. In this paper, we establish the M‐polynomial and NM‐polynomial of some very familiar biopolymers, which are xanthan gum, gellan gum, and polyacrylamide. The uses of these biopolymers can increasingly take the place of traditional admixtures for the application of soil stability and enhancement. We recover the important topological degree‐based indices. Also, we give diverse graphs of topological indices and their relations with the parameters of structures.

A topological index(TI) is a numerical value matching to a graph. It is frequently employed in chemometrics, biomedicines and bioinformatics to forecast various physiochemical attributes and biological activities of a substances. One of the polynomials named as neighborhood M-polynomial (NM-polynomial) which is used to derive numerous degree-based TI’s. Polysaccharide, poly-γ-glutamic acid and poly-l-lysine, which is a well-known biopolymer, It has extraordinary qualities that attracts a great deal of attention in the fields of medicine, the food industry, wastewater treatment, etc. In this we calculate the degree based and neighborhood degree based indices for above-stated biopolymers in consolidate by using. The NM-polynomial and M-polynomial is being utilized to consolidate the degree based and neighborhood degree based indices are calculated for the study.

This study investigates the relevance of physicochemical properties of 34 NSAIDs to their chemical characteristics using total quadratic indices q _k (x) modeled as pseudographs with atomic number and atomic radius weighting schemes, compared against traditional indices modeled using unweighted graphs. The objective was to assess the predictive capabilities of these indices in modeling drug properties. Multiple Ordinary Least Squares (OLS) regression revealed significant multicollinearity in the models. Principal Component Analysis (PCA) was employed to address this issue, leading to a reduction in multicollinearity, although it was accompanied by a slight decrease in model performance metrics such as R ². Despite this, quadratic indices demonstrated competitive performance when compared to traditional indices. Notably, the quadratic indices showed higher relevance in predicting the physicochemical properties complexity (C), molecular weight (MW), refractivity (RV) and polarizability (P) compared to traditional indices. The model validated by parameters like coefficient of determination (R ²), p - value, standard error (S.E), F-statistic and Durbin-Watson (DW) statistics. These results underscore the potential of quadratic indices in enhancing predictive modeling of drug properties, offering improved insights compared to traditional topological indices.