On the Laplacian spectra and the Kirchhoff indices of two types of networks

Abstract

Let G be a connected simple graph. Denoted by the Kirchhoff index of G. In this note, we study the Laplacian spectra of two types of networks and . As a special case, explicit formulas for the Kirchhoff index and number of spanning trees of prisms are obtained. Some other interesting results, such as the expression for the coefficient of the Laplacian characteristic polynomials of cycles, are also derived.