Topological indices are not necessarily invariant to graph labeling

Area of Science:

• * Computational chemistry and cheminformatics.
• * Graph theory applications in chemical sciences.

Background:

• * Molecular descriptors are crucial for quantitative structure-activity relationships (QSAR).
• * Graph-based matrices offer a way to encode molecular topology and properties.
• * The Universal matrix (U) considers vertex degrees and distances for weighted contributions.

Purpose of the Study:

• * To investigate the utility of the Universal matrix (U) as a molecular descriptor.
• * To determine if U-matrix elements can predict physicochemical properties.
• * To assess the invariance of U-matrix descriptors to molecular labeling.

Main Methods:

• * Construction of the Universal matrix (U) using vertex degrees and distances.
• * Analysis of matrix element invariance under different vertex labeling schemes.
• * Correlation analysis between U-matrix elements and physicochemical properties of octanes.

Main Results:

• * Certain U-matrix elements are invariant to vertex labeling, reflecting structural features.
• * Specific matrix elements and their combinations serve as effective descriptors for physicochemical properties.
• * The predictive power of these descriptors was demonstrated for octane isomers.

Conclusions:

• * The Universal matrix (U) provides valuable, structurally relevant molecular descriptors.
• * U-matrix elements demonstrate robustness against arbitrary vertex enumeration.
• * This approach offers a promising method for predicting molecular properties in cheminformatics.