The Kirchhoff Index and the Matching Number

摘要

The Kirchhoff index of a connected (molecular) graph is the sum of the resistance-distances between all unordered pairs of vertices and may also be expressed by its Laplacian eigenvalues. We determine the minimum Kirchhoff index of connected (molecular) graphs in terms of the number of vertices and matching number and characterize the unique extremal graph. The results on the Kirchhoff index are compared with the corresponding results on the Wiener index. (C) 2008 Wiley Periodicals, Inc. Int J Quantum Chem 109: 2978-2981, 2009