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On the relation between W'/W index, hyper-Wiener index, and Wiener numbers
1The Rugjer Boskovic Institute, Zagreb, The Republic of Croatia.
Journal of Chemical Information and Computer Sciences
|June 13, 2000
Summary
This study reveals close relationships between graph invariants like the W'/W index, hyper-Wiener index, and Wiener number in acyclic structures. A new analytical expression for the hyper-Wiener index of trees is also presented.
Area of Science:
- Graph Theory
- Mathematical Chemistry
- Chemical Informatics
Background:
- Graph invariants are crucial for understanding molecular structures.
- The Wiener number and hyper-Wiener index are established molecular descriptors.
- Relationships between various graph invariants, particularly for acyclic structures, warrant further investigation.
Purpose of the Study:
- To analytically demonstrate the close relationship between the W'/W index, hyper-Wiener index, and Wiener number for acyclic structures.
- To derive a general analytical expression for the hyper-Wiener index of trees.
Main Methods:
- Analytical derivation using graph theory principles.
- Focus on acyclic structures (trees).
- Mathematical formulation of graph invariants.
Main Results:
- Established a close relationship between W'/W index, hyper-Wiener index, and Wiener number in trees.
- Derived a general analytical expression for the hyper-Wiener index of trees.
Conclusions:
- The W'/W index, hyper-Wiener index, and Wiener number are interconnected graph invariants for acyclic systems.
- The derived expression provides a new tool for analyzing tree structures in chemical graph theory.