Contraction Formulas for the Kirchhoff and Wiener Indices


Cinkir Z.

MATCH-COMMUNICATIONS IN MATHEMATICAL AND IN COMPUTER CHEMISTRY, cilt.75, ss.169-198, 2016 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 75 Konu: 1
  • Basım Tarihi: 2016
  • Dergi Adı: MATCH-COMMUNICATIONS IN MATHEMATICAL AND IN COMPUTER CHEMISTRY
  • Sayfa Sayısı: ss.169-198

Özet

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.