In this paper, we use the ensemble machine learning technique to evaluate the strength of three supervised machine learning algorithms, namely, the random forest regression (RFR), support vector regression (SVR) and the gradient boosting regression (GBR) in the prediction of physical properties of mental disorder drugs with small dataset. The model was implemented on a dataset of neighborhood degree-based topological indices which served as predictor variables and physical properties of the drugs which served as target variables. To compute the neighborhood degree-based indices, we employed an algorithm that utilizes the canonical SmilES notations of the drugs. The ensemble method identifies the neighborhood third Zagreb index (NM₃(G)) as an efficient predictor of boiling point, flash point and enthalpy of vaporization. The neighborhood Randic index (NR(G)) provides better prediction for molar refractivity, molar volume and polarizability. In the same vein, the neighborhood sum connectivity index (NSC(G)) is an efficient predictor of surface tension while the neighborhood reciprocal Randic index (NRR(G)) is most effective in the prediction of polar surface area. Furthermore, the comparison of the average performance between the ensemble method and the base models (RFR, SVR, GBR) over the neighborhood topological indices shows efficient performance of the individual models across multiple physical properties of mental disorder drugs, when using the neighborhood topological indices as the predictor or input feature. Overall, this research highlights the combination of three supervised machine learning models in an ensemble environment to mitigating the challenges associated with small datasets when applying machine learning models in QSPR analysis.

Quantitative Structure-Property Relationship (QSPR) modeling is one of the novel ways of predicting the physicochemical properties of a drug through its molecular descriptor (topological index (TI)). This study aims to predict the physical properties of antibacterial drugs by utilizing neighborhood sum degree TI (NTI) and employing two regression models namely, simple linear regression (LR) and support vector regression (SVR) as a machine learning model. In contrast to traditional methods of computing TI, we utilize the simplified molecular-input line-entry system (SMILES) of antibacterial drug compounds to compute the numerical parameters linked to antibacterial drug compounds. To enhance the predictive power of the QSPR model, we employ backward elimination method for LR model while incorporating sequential backward search selection (SBSS) technique for the SVR model. The study demonstrated that the SVR model outperformed the LR model, showcasing the SVR model’s ability to handle small datasets effectively. Hyperparameter tuning and the SBSS method were crucial in enhancing the SVR model’s performance by iteratively excluding non-informative features, thereby reducing error metrics and optimizing the model. The study identified the predictive capability of NTIs for various properties, including boiling point, melting point, flash point, enthalpy of vaporization, molar refraction, polarization, surface tension, and molar volume. The optimized SVR model showed high prediction accuracy for drugs such as Tobramycin, Gentamicin, Linezolid, Moxifloxacin, and Cilastatin, with predicted values closely matching actual physical properties. The results of our research highlight the significance of integrating advanced machine learning algorithms into drug property prediction leading to the optimization of drug design and discovery process.

Let (G,∗) be a finite group and S={x∈G|x≠x⁻¹} be a subset of G containing its non-self invertible elements. The inverse graph of G denoted by Γ(G) is a graph whose set of vertices coincides with G such that two distinct vertices x and y are adjacent if either x∗y∈S or y∗x∈S. In this paper, we study the energy of the dihedral and symmetric groups, we show that if G is a finite non-abelian group with exactly two non-self invertible elements, then the associated inverse graph Γ(G) is never a complete bipartite graph. Furthermore, we establish the isomorphism between the inverse graphs of a subgroup D_p of the dihedral group D_n of order 2p and subgroup S_k of the symmetric groups S_n of order k! such that $2p = n!~(p,n,k \geq 3~\text {and}~p,n,k \in \mathbb {Z}^{+}).$2 p = n ! ( p , n , k ≥ 3 and p , n , k ∈ ℤ + ) .