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An efficient method for decomposition of regular structures using graph products. (English) Zbl 1075.74539
Summary: 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.
MSC:
74H15Numerical approximation of solutions for dynamical problems in solid mechanics
74H45Vibrations (dynamical problems in solid mechanics)
74S30Other numerical methods in solid mechanics
05C90Applications of graph theory