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 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 111 Issue: 15
  • Publication Date: 2011
  • Doi Number: 10.1002/qua.22942
  • Journal Name: INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.4030-4041
  • Abdullah Gül University Affiliated: No

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