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Laplacian matrices of product graphs: applications in structural mechanics

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Abstract

Graph products have been studied extensively in the recent decade and applied to many problems in structural mechanics, including configuration processing, parallel computing, and optimal analysis of structures. In this paper, a general theorem is proved for the formation of the Laplacian matrices of product graphs. Using this theorem, exact relationships are derived for eigensolution of Laplacian matrices of product graphs. For the cases where no exact formula is available for calculating the eigenvalues of these matrices, some explanations are provided for the approximate approaches. Applications of the Laplacian matrices of product graphs in structural mechanics are illustrated via some examples.

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Authors and Affiliations

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

    A. Kaveh & B. Alinejad

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  1. A. Kaveh
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  2. B. Alinejad
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Correspondence to A. Kaveh.

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Kaveh, A., Alinejad, B. Laplacian matrices of product graphs: applications in structural mechanics. Acta Mech 222, 331–350 (2011). https://doi.org/10.1007/s00707-011-0540-9

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  • DOI: https://doi.org/10.1007/s00707-011-0540-9

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