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Trees with Cantor Eigenvalue Distribution

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We study a family of trees with degree k at all interior nodes and degree 1 at boundary nodes. The eigenvalues of the adjacency matrix have high multiplicities. As the trees grow, the graphs of those eigenvalues approach a piecewise-constant “Cantor function.” For each value of , we will find the fraction of the eigenvalues that are given by .
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Document Type: Research Article

Publication date: February 1, 2003

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