Overall molecular descriptors. 3. Overall Zagreb indices

Area of Science:

• * Computational Chemistry
• * Cheminformatics
• * Mathematical Chemistry

Background:

• * Molecular topology characterization relies on graph invariants.
• * Previous work utilized adjacency and distance matrices for overall descriptors.
• * Current research extends this by incorporating vertex degree functions.

Purpose of the Study:

• * To develop and analyze overall versions of the first and second Zagreb indices.
• * To assess the applicability of these new topological descriptors.
• * To compare their predictive power against existing methods.

Main Methods:

• * Calculation of graph invariants for all molecular subgraphs.
• * Definition of cumulative topological descriptors and eth-order terms.
• * Application of multilinear regression models to physicochemical properties of alkanes.

Main Results:

• * Detailed analysis of overall Zagreb indices.
• * Successful derivation of regression models for ten alkane properties.
• * Comparison of predictive performance with molecular connectivity and overall connectivity indices.

Conclusions:

• * Overall Zagreb indices offer a novel approach to molecular topological characterization.
• * These descriptors demonstrate potential in predicting physicochemical properties.
• * The findings contribute to the advancement of structure-property relationship studies.