Contraction Formulas for the Kirchhoff and Wiener Indices

Cinkir Z.

MATCH-COMMUNICATIONS IN MATHEMATICAL AND IN COMPUTER CHEMISTRY, cilt.75, sa.1, ss.169-198, 2016 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 75 Sayı: 1
  • Basım Tarihi: 2016
  • Dergi Adı: MATCH-COMMUNICATIONS IN MATHEMATICAL AND IN COMPUTER CHEMISTRY
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.169-198
  • Abdullah Gül Üniversitesi Adresli: Evet

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.