Kirchhoff index of a class of polygon networks

Abstract

The Kirchhoff index is a novel distance-based topological index corresponding to networks, which is the sum of resistance distances between all pairs of nodes. It plays an important role in describing the flow of a network. In this paper, we propose a polygon network model and derive the eigenvalue evolving rule between two generations of the network, and thus obtain the exact Kirchhoff index using the spectral graph theory.