the laplacian spectrum of the generalized n-prism networks

‎the laplacian eigenvalues and polynomials of the networks play an essential role in understanding the relations between the topology and the dynamic of networks‎. ‎generally‎, ‎computation of the laplacian spectrum of a network is a hard problem and there are just a few classes of graphs with the property that their spectra have been completely computed‎. ‎laplacian spectrum for n-prism networks was investigated in [liu et al.‎, ‎neurocomputing 198 (2016) 69-73]‎. ‎in this paper‎, ‎we give a method for calculating the eigenvalues and characteristic polynomial of the laplacian matrix of a generalized n-prism network‎. ‎we show how such large networks can be constructed from small graphs by using graph products‎. ‎moreover‎, ‎our results are used to obtain the kirchhoff index and the number of the spanning trees in the generalized n-prism networks‎. ‎we also give some examples of applications‎, ‎that explain the usefulness and efficiency of the proposed method‎.