This work initiates a concept of reduced reverse degree based \(\mathcal {RR_D\,M}\)-Polynomial for a graph, and differential and integral operators by using this \(\mathcal {RR_D\,M}\)-Polynomial. In this study twelve reduced reverse degree-based topological descriptors are formulated using the \(\mathcal {RR_D\,M}\)-Polynomial. The topological descriptors, denoted as \(\mathbb{T}\mathbb{D}\)’s, are numerical invariants that offer significant insights into the molecular topology of a molecular graph. These descriptors are essential for conducting QSPR investigations and accurately estimating physicochemical attributes. The structural and algebraic characteristics of the graphene and graphdiyne are studied to apply this methodology. The study involves the analysis and estimation of Reduced reverse degree-based topological descriptors and physicochemical features of graphene derivatives using best-fit quadratic regression models. This work opens up new directions for scientists and researchers to pursue, taking them into new fields of study.

In the present work, the physicochemical characteristics of important anti-tuberculosis (TB) drugs such as isoniazid, pyrazinamide, ethambutol, ethionamide, linezolid, and levofloxacin are explored using extended energy-based topological indexes. Based on the molecules of the drugs, we calculate the extended energies of many widely recognized indexes such as Zagreb Second Index, Harmonic Index, Randic Index, Sombor Index, Reduced Sombor Index, and Average Sombor Index. All the calculations are done using Python, and the rigorous algorithmic implementation in the form of matrix formulation and computation of the eigenvalue is also given for reproducibility. We use the linear, quadratic, and logarithmic regression models to predict nine important physicochemical parameters: the boiling point, the melting point, the flash point, the molar refractivity, the polarizability, the molar volume, the molecular weight, the logarithm of the partition coefficient, and the surface area. Among the three models, the quadratic regression always yields the best predictability, as reflected in the largest coefficient of determination (\(R^2\)) as well as the minimum root mean square error (RMSE) values. Visual analyses such as heatmaps, scatter plot matrices, bar charts, and regression plots are employed to complement the numerical findings. Also, a rigorous discourse about model validity, model significance, and limitations is discussed. The entire source code and dataset are made available through GitHub to allow verification and transparency. The Python-based QSPR methodology, in addition to elucidating the high correlation of the topological descriptors with the properties of drugs, offers a drug design and optimization process in pharmaceutical research in an efficient way.

QSPR mathematically links physicochemical properties with the structure of a molecule. The physicochemical properties of chemical molecules can be predicted using topological indices. It is an effective method for eliminating costly and time-consuming laboratory tests. We established a QSPR between mev-degree and mve-degree-based indices and the physical properties of benzenoid hydrocarbons. To compute these indices, we designed a program using Maple software and the correlation between indices and physical properties was developed using the SPSS software. Our study reveals that the mve-degree-based sum-connectivity \((\chi ^{mve})\) and atom bond connectivity (\(ABC^{mve}\)) index, mev-degree-based Randić (\(R^{mev}\)) and Zagreb (\(M^{mev}\)) index are the three most significant parameters and have good prediction ability for the physicochemical properties. We examined that \(R^{mev}\) predicts the molar refractivity and boiling point, \({\chi }^{mve}\) predicts the LogP and enthalpy, \(ABC^{mve}\) predicts the molecular weight, \(M^{mev}\) predicts the Gibb’s energy, Pie-electron energy and Henry’s law. Moreover, we computed the indices for the linear [n]-phenylen.

In this paper, the Yang transform Adomian decomposition method (YTADM) is employed in the solution of nonlinear time‐fractional coupled Burgers equations. The technique solves the fractional and nonlinear terms successfully via the Adomian decomposition of the Yang transform. Illustrative examples are given, which show the accuracy and ease of implementation of the method. The results show that the YTADM method gives good, reliable results and is very accurate, so that its solutions agree well with the exact solution. Finally, tables and graphs are shown, which illustrate the behavior of the solutions found.

In this article, we present the concept of extended Seidel energy by employing a generalized extended matrix to study various molecular properties, including the Kovats retention index, boiling point, enthalpy of formation, entropy, acentric factor, and octanol-water partition coefficient. Our research broadens the scope of energy matrices in graph theory, with a particular emphasis on Sombor energy, reduced Sombor energy, average Sombor energy, Banhatti Sombor energy and reduced Banhatti Sombor energy. We examined the correlation of these graph-based energy descriptors with the thermodynamic properties of Benzenoid hydrocarbons (BHC), uncovering strong relationships between these indices and different molecular attributes. These results provide valuable insights into the predictive potential of graph energies in modeling the thermodynamic behavior of polycyclic aromatic hydrocarbons.

1. The ultrasonic-guided waves testing has become a common technique in the non-destructive testing (NDT) because of its capability of inspecting long distances to detect structural changes or defe...