Kirchhoff index of linear pentagonal chains

Abstract

Abstract The resistance distance r ij between two vertices v i and v j of a connected graph G is computed as the effective resistance between nodes i and j in the corresponding network constructed from G by replacing each edge of G with a unit resistor. The Kirchhoff index Kf( G ) is the sum of resistance distances between all pairs of vertices. In this article, following the method of Yang and Zhang in the proof of the Kirchhoff index of liner hexagonal chain, we obtain the closed‐form formulae of the Kirchhoff index of liner pentagonal chain P n in terms of its Laplacian spectrum. Finally, we show that the Kirchhoff index of P n is approximately one half of its Wiener index. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010