Contraction Formulas for the Kirchhoff and Wiener Indices

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Cinkir Z.

MATCH-COMMUNICATIONS IN MATHEMATICAL AND IN COMPUTER CHEMISTRY, vol.75, no.1, pp.169-198, 2016 (SCI-Expanded)

• Publication Type: Article / Article
• Volume: 75 Issue: 1
• Publication Date: 2016
• Journal Name: MATCH-COMMUNICATIONS IN MATHEMATICAL AND IN COMPUTER CHEMISTRY
• Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
• Page Numbers: pp.169-198
• Abdullah Gül University Affiliated: Yes

Abstract

We relate the Kirchhoff index with some other metrized graph invariants. We establish several contraction formulas for the Kirchhoff index. We use these contraction formulas and certain edge densities to give new upper and lower bounds to the Kirchhoff index for any connected graph. As an another application of our contraction formulas when the graph is a tree, we derive new formulas as well as previously known formulas for the Wiener index with new proofs.