Interrelations of graph distance measures based on topological indices

Area of Science:

• Graph theory
• Mathematical chemistry
• Computational biology

Background:

• Topological indices are crucial for understanding molecular structure and properties.
• Existing research often focuses on individual indices, with limited exploration of their interrelations.
• Novel graph distance measures based on topological indices warrant investigation.

Purpose of the Study:

• To derive and analyze interrelations between various graph distance measures, including topological indices.
• To investigate the properties and quality of these measures through numerical studies.
• To explore potential applications in chemoinformatics and computational biology.

Main Methods:

• Derivation of inequalities to establish interrelations between graph distance measures.
• Utilizing topological indices such as the Wiener index and Randić index.
• Employing eigenvalue-based quantities and graph entropies in the analysis.
• Conducting numerical studies to assess measure properties and quality.

Main Results:

• Established novel interrelations between graph distance measures based on topological indices.
• Demonstrated the utility of inequalities in understanding these relationships.
• Numerical studies provided insights into the behavior and effectiveness of the measures.

Conclusions:

• The derived interrelations offer a deeper understanding of graph distance measures.
• The findings have potential applications in structural analysis within chemoinformatics and computational biology.
• Further research can build upon these interrelations for advanced network and molecular studies.