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Eigenvalues of the adjacency and Laplacian matrices for modified regular structural models
Author(s) -
Kaveh A.,
Rahami H.
Publication year - 2010
Publication title -
international journal for numerical methods in biomedical engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.741
H-Index - 63
eISSN - 2040-7947
pISSN - 2040-7939
DOI - 10.1002/cnm.1269
Subject(s) - adjacency matrix , eigenvalues and eigenvectors , graph , adjacency list , mathematics , finite element method , graph energy , laplace operator , regular graph , discrete mathematics , combinatorics , voltage graph , engineering , mathematical analysis , line graph , structural engineering , physics , quantum mechanics
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. Copyright © 2009 John Wiley & Sons, Ltd.