Computation of Kirchhoff Index in Generalized Ladders

Abstract

A connected graph G is viewed as an electrical network N by replacing each edge of G with a unit resistor. The Kirchhoff index of G is a structure-descriptor based on effective resistance of N. The generalized ladder is a subdivision graph of ladder graph. By using the properties of the Chebyshev polynomials, Laplace Theorem and so on, we obtained closed form expressions of Kirchhoff indexes for the generalized straight and generalized cyclic ladders, which generalize the results of linear quadrangular chain and linear hexagonal chain.