Eigenvectors of the De Bruijn Graph Laplacian: A Natural Basis for the Cut and Cycle Space

We study the Laplacian of the undirected De Bruijn graph over an alphabet \(A\) of order \(k\). While the eigenvalues of this Laplacian were found in 1998 by Delorme and Tillich [1], an explicit description of its eigenvectors has remained elusive. In this work, we find these eigenvectors in closed...

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Veröffentlicht in:	arXiv.org 2024-10
Hauptverfasser:	Philippakis, Anthony, Mallinar, Neil, Pandit, Parthe, Belkin, Mikhail
Format:	Artikel
Sprache:	eng
Schlagworte:	Eigenvalues Eigenvectors Fourier transforms Graph theory Graphs
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