Sombor-based graph-theoretic framework for the structural characterization of neuro-metabolic organic acids

Neuro-metabolic organic acids are essential endogenous metabolites involved in brain-associated biochemical pathways and exhibit considerable structural diversity. Despite their biological importance these molecules have received limited attention from the perspective of modern Sombor-based chemical graph theory and a systematic topological characterization using Sombor-type descriptors has not previously been reported.

A unified Sombor-based graph-theoretic framework is developed for the structural characterization of eight endogenous neuro-metabolic organic acids using hydrogen-suppressed molecular graphs. Six complementary Sombor-type descriptors namely the classical, reduced, average, elliptic, Euler and reverse Sombor indices are computed and comparatively analyzed. In addition five original graph-theoretic results are established to explain the influence of functional-group density, perturbation sensitivity, branching complexity, heteroatom-associated connectivity and degree heterogeneity on descriptor behavior.

The proposed framework effectively distinguishes structurally diverse neuro-metabolic organic acids. Molecular graphs with greater functional-group density, richer branching architecture, enhanced heteroatom-associated connectivity and higher degree heterogeneity consistently exhibit larger Sombor-type descriptor values. The numerical results illustrate consistency with the proposed graph-theoretic framework and provide a multidimensional characterization of molecular structural organization.

Compared with classical degree-based descriptors such as the Zagreb and Randić indices, Sombor-type descriptors provide greater sensitivity to branching, connectivity heterogeneity and structurally influential edge configurations while retaining computational simplicity.

This study extends the application of Sombor-based chemical graph theory to neuro-metabolic organic acids and introduces a unified framework integrating descriptor analysis with original graph-theoretic results for comparative molecular structural characterization.