A Graph-Theoretic Computation of the Partition Dimension of Molecular Graphs for Anti-Myocardial Infarction Drugs Using Graph Neural Networks
Patullayeva K. Ashfaq S. Anjam Y.N. Khan H. Tahir M.A.
February 2026Multidisciplinary Digital Publishing Institute (MDPI)
Symmetry
2026#18Issue 2
This study aims to investigate the computation of the partition dimension of various anti-myocardial infarction drugs, a graph-theoretical invariant of molecular graphs representing these drugs, for understanding and computationally characterizing structural properties of molecular networks. To improve the computational modeling of this topological invariant, advanced neural network techniques, specifically graph neural networks (GNNs) and deep neural networks (DNNs), are adopted. The GNN captures topological and molecular connection features from the molecular graph structures, which are then input into the DNN model. The DNN further processes these features to estimate the partition dimension, evaluating training performance, performing regression analysis, and producing error histograms. The model’s predictions are validated against reference values. Moreover, by analyzing the role that symmetry plays in determining the calculation of partition dimension, studying how the GNN takes advantage of permutation invariance concept related to symmetry principles to provide the DNN with symmetry-invariant features, and relating the degree of molecular symmetry to the predictive model’s accuracy and performance, its structural interpretation rather than direct chemical behavior. This dual-model approach permits a comprehensive evaluation of the model’s effectiveness in apprehending the structural characteristics of molecular graphs derived from drug molecules. The results are explicated in detail, focused on prediction accuracy, error distributions, and regression results. Moreover, this graph-theoretical metric analysis of partition dimension supports structure-based drug analysis and computational modeling, rather than direct prediction of pharmacokinetic properties, by integrating artificial neural network applications into pharmaceutical research.
chemical graph theory , deep neural networks , graph neural networks , partition resolvability
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Department of Mathematics and Natural Sciences, SDU, Almaty, 040900, Kazakhstan
Department of Applied Sciences, National Textile University, Faisalabad, 37610, Pakistan
School of Digital Technologies, Narxoz University, Almaty, 050035, Kazakhstan
Department of Mathematics and Natural Sciences
Department of Applied Sciences
School of Digital Technologies
10 лет помогаем публиковать статьи Международный издатель
Книга Публикация научной статьи Волощук 2026 Book Publication of a scientific article 2026