Trees with cantor eigenvalue distribution

摘要

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 m, we will find the fraction of the eigenvalues that are given by lambda = 2rootk -1 cos(pim). [References: 11]