An efficient method for decomposition of regular structures using graph products

In this paper an efficient method is presented for calculating the eigenvalues of regular structural models. A structural model is called regular if they can be viewed as the direct or strong Cartesian product of some simple graphs known as their generators . The eigenvalues of the adjacency and Laplacian matrices for a regular graph model are easily obtained by the evaluation of eigenvalues of its generators. The second eigenvalue of the Laplacian of a graph is also obtained using a much faster and much simple approach than the existing methods.