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A Distributed Algorithm for the Assignment of the Laplacian Spectrum for Path Graphs

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  • Gianfranco Parlangeli

    (Department of Engineering for Innovation, University of Salento, via per Monteroni, 73100 Lecce, Italy)

Abstract

In this paper, we bring forward a distributed algorithm for the assignment of a prescribed Laplacian spectrum for path graphs by means of asymmetric weight assignment. We first describe the meaningfulness and the relevance of this mathematical setting in modern technological applications, and some examples are reported, revealing its practical usefulness in a variety of applications. Then, the solution is derived both theoretically and through an algorithm. Special attention is devoted to a distributed implementation of the main algorithm, which is a valuable feature for several modern applications. Finally, the positivity is discussed, which is revealed to be a consequence of the strict interlacing property.

Suggested Citation

  • Gianfranco Parlangeli, 2023. "A Distributed Algorithm for the Assignment of the Laplacian Spectrum for Path Graphs," Mathematics, MDPI, vol. 11(10), pages 1-12, May.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:10:p:2359-:d:1150420
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    References listed on IDEAS

    as
    1. Wei, Ying & Dai, Hua, 2015. "An inverse eigenvalue problem for Jacobi matrix," Applied Mathematics and Computation, Elsevier, vol. 251(C), pages 633-642.
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