Chemical applicability and predictive potential of certain graphical indices for determining structure-property relationships in polycrystalline acid magenta (C20H17N3Na2O9S3)

Acid Magenta, also known as Fuchsine acid, is a polycrystalline material with an anorthic structure that stands out for its eco-friendliness, cost-effectiveness, and versatility. Widely used in histology for cellular differentiation and across various industrial applications, Acid Magenta's detailed molecular understanding and prediction of physicochemical properties hold significant value. Despite its relevance, research focused on the molecular topological modeling of Acid Magenta remains limited. This gap presents a unique opportunity to develop accurate and reliable topological descriptions of this molecular structure, which could significantly benefit industrial applications. This study aims to bridge the existing gap in topological modeling of Acid Magenta through a Quantitative Structure-Property Relationship (QSPR) and Quantitative Structure-Activity Relationship (QSAR) analysis, potentially enhancing its industrial utility. Utilizing efficient vertex partitioning techniques from chemical graph theory, we developed closed-form expressions for crucial topological descriptors, including the 1st multiplicative Zagreb index, 1st exponential Zagreb index, forgotten topological index, inverse degree index, 1st Zagreb index, multiplicative exponential Zagreb index and modified 1st Zagreb index. These derived indices were systematically evaluated to assess their impact on the structural properties of Acid Magenta. To further test predictive potential, the model applied linear fitting to key physicochemical properties of 18 octane isomers. Findings reveal that the indices 1st Zagreb index, Forgotten index, and Inverse degree index exhibit strong predictive correlations with these properties, particularly for entropy, the acentric factor, and enthalpy of vaporization (HVAP). The robust predictive performance of these indices underscores their potential as efficient alternatives to experimental testing for future QSAR/QSPR analysis, paving the way for new applications in environmental and industrial settings.