Applications of Laplacian spectra for n-prism networks

• We propose the structure of n-prism networks.
• We calculate the Laplacian spectra of n-prism networks.
• We deduce expressions for product and sum of reciprocals of all nonzero Laplacian-eigenvalues.
• Kirchhoff index, GMFPT, average path length and the number of spanning trees are obtained.

In this paper, the properties of the Laplacian matrices for the n-prism networks are investigated. We calculate the Laplacian spectra of n-prism graphs which are both planar and polyhedral. In particular, we derive the analytical expressions for the product and the sum of the reciprocals of all nonzero Laplacian eigenvalues. Moreover, these results are used to handle various problems that often arise in the study of networks including Kirchhoff index, global mean-first passage time, average path length and the number of spanning trees. These consequences improve and extend the earlier results.