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

Area of Science:

• * Computational Chemistry
• * Chemoinformatics
• * Graph Theory

Background:

• * Neuro-metabolic organic acids are vital endogenous metabolites in brain biochemistry.
• * Limited research exists on their topological characterization using Sombor-based chemical graph theory.
• * A systematic study of these molecules using Sombor-type descriptors was previously unreported.

Purpose of the Study:

• * To develop a unified Sombor-based graph-theoretic framework for characterizing neuro-metabolic organic acids.
• * To compute and analyze six complementary Sombor-type descriptors.
• * To establish graph-theoretic results explaining descriptor behavior based on molecular features.

Main Methods:

• * Utilized hydrogen-suppressed molecular graphs for eight endogenous neuro-metabolic organic acids.
• * Computed classical, reduced, average, elliptic, Euler, and reverse Sombor indices.
• * Established five original graph-theoretic results to analyze descriptor influences.

Main Results:

• * The framework successfully distinguishes structurally diverse neuro-metabolic organic acids.
• * Higher functional-group density, branching, heteroatom connectivity, and degree heterogeneity correlate with larger Sombor-type descriptor values.
• * Numerical results confirm the framework's consistency and provide multidimensional structural characterization.

Conclusions:

• * Extends Sombor-based chemical graph theory applications to neuro-metabolic organic acids.
• * Introduces a unified framework for comparative molecular structural characterization.
• * Integrates descriptor analysis with novel graph-theoretic insights.