Eigenvalues of the adjacency and Laplacian matrices for modified regular structural models. (English) Zbl 1207.05119
Summary: The graph model of many space structures and finite element models can be formed using graph products. These structures are known as regular structures. 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 a modified regular structure. 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.
MSC:
| 05C50 | Graphs and linear algebra (matrices, eigenvalues, etc.) |
| 05C76 | Graph operations (line graphs, products, etc.) |
Keywords:
modified graph products; Cartesian product; strong Cartesian product; eigenvalues; space structures; modified regular structureReferences:
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