Deletion and Contraction Identities for the Resistance Values and the Kirchhoff Index


Cinkir Z.

INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, vol.111, no.15, pp.4030-4041, 2011 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 111 Issue: 15
  • Publication Date: 2011
  • Doi Number: 10.1002/qua.22942
  • Title of Journal : INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY
  • Page Numbers: pp.4030-4041

Abstract

We establish identities, which we call deletion and contraction identities, for the resistance values on an electrical network. As an application of these identities, we give an upper bound to the Kirchhoff index of a molecular graph. Our upper bound, expressed in terms of the set of vertices and the edge connectivity of the graph, improves previously known upper bounds. (C) 2010 Wiley Periodicals, Inc. Int J Quantum Chem 111: 4030-4041, 2011