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

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

Mathematics, 2023, vol. 11, issue 10, 1-12

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.

Keywords: Laplacian eigenvalues; path graphs; inverse eigenvalue problems (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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