GRAPH PRODUCTS FOR DOMAIN DECOMPOSITION OF REGULAR STRUCTURES

In this paper, efficient methods are presented for calculating the eigenvalues of regular structural models. The eigenvalues of the adjacency and Laplacian matrices for a regular graph model are easily obtained by evaluation of the eigenvalues of its generators. The second eigenvalue of the Laplacian of a graph is also obtained using a much faster and much simpler approach than the existing methods. Once the second eigenvector v2 of the Laplacian matrix is calculated, the bisection of the model can be performed. This is achieved, by arranging the entries of v2 in an ascending order and partitioning the nodes into two subsets according to their occurrence in v2.

Keywords:

graph product , regular structures , second eigenvalue , decomposition , Cartesian product , strong Cartesian product , direct product