Wiener index extension by counting even/odd graph distances.

Area of Science:

• * Cheminformatics and computational chemistry.
• * Quantitative structure-activity/property relationships (QSAR/QSPR).

Background:

• * Chemical structures are numerically characterized by topological indices, such as the Wiener index (W).
• * Topological indices are crucial in drug design, database screening, and assessing chemical similarity and diversity.

Purpose of the Study:

• * To introduce novel topological indices derived from partitioning the Wiener index based on even and odd molecular graph distances.
• * To generalize these indices with optimizable weighting exponents for QSAR/QSPR modeling.
• * To evaluate the performance of these new indices in predicting physical properties of alkanes.

Main Methods:

• * Development of new topological indices by analyzing even and odd counts of distances in molecular graphs.
• * Generalization of indices using weighting exponents for QSPR model optimization.
• * Application and testing of the novel indices in QSPR models for various physical properties of alkanes.

Main Results:

• * The proposed even/odd distance topological indices provide improved correlations for QSPR models.
• * These novel indices demonstrate enhanced predictive power for properties like boiling temperature, heat capacity, and density in alkanes.
• * Optimized weighting exponents further refine the predictive accuracy of the models.

Conclusions:

• * The novel even/odd distance-based topological indices represent a significant advancement in cheminformatics.
• * These indices offer a more nuanced approach to characterizing molecular structures for property prediction.
• * The developed indices show strong potential for application in drug discovery and materials science.