Cinkir, Zubeyir2021-08-262021-08-2620160340-6253https://hdl.handle.net/20.500.12573/954This work is supported by The Scientific and Technological Research Council of Turkey-TUBITAK (Project No: 110T686) and by BAGEP of The Science Academy. Z. C. thanks anonymous referees for their valuable suggestions.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.enginfo:eu-repo/semantics/closedAccessTREESRESISTANCE DISTANCETAU CONSTANTMETRIZED GRAPHarticleVolume 75 Issue 1 Page 169-198