Space Structures and Graph Theory

In this paper, efficient methods are presented for calculating the eigenvalues of space structural models. The eigenvalues of the adjacency and Laplacian matrices for a 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 can be achieved by arranging the entries of v2 in an ascending order and partitioning the nodes into two subsets according to their occurrence in v2.

کلیدواژه ها:

Space structures ، graph theory ، algebraic graph theory ، graph products ، second eigenvalue ، decomposition