Eigenvalues of the adjacency and Laplacian matrices for modified regular structural models

The graph model of many space structures and finite element models can be formed using graph products. These structures are known asregularstructures. Methods for calculating the eigenvalues of the matrices corresponding to these models are already investigated. In practice for some structural models the addition of some nodes and members to the graph product is required. When such a node and the incident members are added to a regular model, it becomes amodified regularstructure. In this paper the eigenproblem of the matrices corresponding to these models is studied. The necessary formulations are derived and examples are presented to illustrate the practical value of the presented approach.