Contraction Formulas For Kirchhoff And Wiener Indices
Zubeyir Cinkir
TL;DR
This paper develops contraction formulas for Kirchhoff and Wiener indices, linking them to other graph invariants, and provides new proofs and formulas for these indices, especially in trees.
Contribution
It introduces new contraction formulas for Kirchhoff index and derives novel Wiener index formulas using these methods.
Findings
Contraction formulas for Kirchhoff index established.
New Wiener index formulas derived for trees.
Connections made between Kirchhoff index and other graph invariants.
Abstract
We establish several contraction formulas for Kirchhoff index. We relate Kirchhoff index with some other metrized graph invariants. By applying our contraction formulas successively when the graph is a tree, we derive new formulas for Wiener index and obtain some previously known Wiener index formulas with new proofs.
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Taxonomy
TopicsTopological and Geometric Data Analysis · Graph theory and applications · Gene Regulatory Network Analysis