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Abstract A generalized Fourier analysis on arbitrary graphs calls for a detailed knowledge of the eigenvectors of the graph Laplacian. Using the symmetries of the Cayley tree, we recursively construct… Click to show full abstract
Abstract A generalized Fourier analysis on arbitrary graphs calls for a detailed knowledge of the eigenvectors of the graph Laplacian. Using the symmetries of the Cayley tree, we recursively construct the family of eigenvectors with exponentially growing eigenspaces, associated with eigenvalues in the lower part of the spectrum. The spectral gap decays exponentially with the tree size, for large trees. The eigenvalues and eigenvectors obey recursion relations which arise from the nested geometry of the tree.
Keywords:
construction eigenvectors;
graph laplacian;
eigenvectors eigenvalues;
cayley tree;
explicit construction
Journal Title: Linear Algebra and its Applications
Year Published: 2020
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Journal Title: Linear Algebra and its Applications
Year Published: 2020
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!