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Inequalities between degree- and distance-based graph invariants.
1COMSATS Institute of Information Technology, Lahore, Pakistan.
Journal of Inequalities and Applications
|March 2, 2018
Summary
This study explores inequalities between degree-based and distance-based topological indices. It derives new relationships, enhancing the comparative analysis of these graph invariants.
Area of Science:
- Graph theory
- Chemical graph theory
- Combinatorics
Background:
- Topological indices are numerical descriptors of molecular graphs.
- They are classified into degree-based and distance-based indices.
- Inequalities are crucial for understanding the relationships between different topological indices.
Purpose of the Study:
- To conduct a relative study of degree-based and distance-based topological indices.
- To derive new inequalities connecting these two classes of indices.
- To enhance the comparative analysis of topological indices in graph theory.
Main Methods:
- Derivation of mathematical inequalities.
- Comparative analysis of selected degree-based indices (Randić connectivity, GA, ABC, harmonic).
- Comparative analysis of selected distance-based indices (eccentric connectivity, connective eccentric, augmented eccentric connectivity, Wiener, third ABC).
Main Results:
- Established novel inequalities between specific degree-based and distance-based topological indices.
- Demonstrated the utility of inequalities for relative study of topological indices.
- Provided a framework for further research into the relationships between graph invariants.
Conclusions:
- Inequalities offer a powerful tool for the relative study of topological indices.
- The derived inequalities contribute to a deeper understanding of graph structure properties.
- This research bridges the gap between degree-based and distance-based topological indices.
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