Vertex Degree Weighted Path Indices

Area of Science:

• Computational Chemistry
• Cheminformatics
• Quantitative Structure-Property Relationships (QSPR)

Background:

• Topological indices are crucial for predicting molecular properties.
• Vertex degree weighted path indices offer a promising approach for characterizing molecular structure.
• Octanes represent a fundamental class of hydrocarbons with diverse physicochemical properties.

Purpose of the Study:

• To evaluate the efficacy of vertex degree weighted path indices (P(N)) in predicting physicochemical properties of octanes.
• To explore the synergistic effects of combining these indices through mutual optimization.
• To investigate the performance enhancement achieved by integrating Universal matrix elements.

Main Methods:

• Calculation of various vertex degree weighted path indices (P(1) to P(4)).
• Application of mutual optimization techniques for index combinations.
• Integration of Universal matrix elements into optimized index combinations.
• Correlation analysis (R-value) to assess predictive accuracy.

Main Results:

• Individual vertex degree weighted path indices (P(1)-P(4)) showed good predictive power for octane properties (|R| up to 0.999).
• Mutually optimized combinations of P(1)-P(4) indices improved predictions (worst case R > 0.9).
• The best predictive accuracy (R = 0.994) was achieved using mutually optimized combinations of selected indices with Universal matrix elements.
• Certain vertex degree weighted path one indices generated regular sequences for octane isomers with increasing branching.

Conclusions:

• Vertex degree weighted path indices are effective descriptors for octane physicochemical properties.
• Mutual optimization significantly enhances the predictive capability of these topological indices.
• Combining optimized indices with Universal matrix elements provides superior QSPR models for octanes.