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Combinatorial optimization of special graphs for nodal ordering and graph partitioning

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Abstract

There are numerous applications of graph theory and algebraic graph theory in combinatorial optimization and optimal structural analysis. In this paper, a new canonical form as well as its relation with four structural models often encountered in practice and their corresponding graphs are presented. Furthermore, the block diagonalization of this form, which is performed using three Kronecker products and unsymmetric matrices, is studied. This block diagonalization leads to an efficient method for the eigensolution of adjacency and Laplacian matrices of special graphs. The eigenvalues and eigenvectors are used for efficient nodal ordering and partitioning of large structural models. The present method is far more simple than any existing general approach.

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Authors and Affiliations

  1. Centre of Excellence for Fundamental Studies in Structural Engineering, Iran University of Science and Technology, Tehran 16, Iran

    A. Kaveh

  2. Department of Civil Engineering, University of Tabriz, Tabriz, Iran

    K. Koohestani

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  1. A. Kaveh
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  2. K. Koohestani
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Correspondence to A. Kaveh.

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Kaveh, A., Koohestani, K. Combinatorial optimization of special graphs for nodal ordering and graph partitioning. Acta Mech 207, 95–108 (2009). https://doi.org/10.1007/s00707-008-0107-6

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  • DOI: https://doi.org/10.1007/s00707-008-0107-6

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