Topological atomic displacements, Kirchhoff and Wiener indices of molecules

Ernesto Estrada, Naomichi Hatano

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We provide a physical interpretation of the Kirchhoff index of any molecules as well as of the Wiener index of acyclic ones. For the purpose, we use a local vertex invariant that is obtained from first principles and describes the atomic displacements due to small vibrations/oscillations of atoms from their equilibrium positions. In addition, we show that the topological atomic displacements correlate with the temperature factors (B-factors) of atoms obtained by X-ray crystallography for both organic molecules and biological macromolecules.
Original languageEnglish
Pages (from-to)166-170
Number of pages4
JournalChemical Physics Letters
Issue number4-6
Early online date4 Jan 2010
Publication statusPublished - 12 Feb 2010


  • topological
  • atomic
  • displacements
  • Kirchoff and Wiener indices
  • molecules


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