Limit points for normalized Laplacian eigenvalues

Abstract

Limit points for the positive eigenvalues of the normalized Laplacian matrix of a graph are considered.Specifically, it is shown that the set of limit points for the j-th smallest such eigenvalues is equal to [0, 1], while the set of limit points for the j-th largest such eigenvalues is
equal to [1, 2].Limit points for certain functions of the eigenvalues, motivated by considerations for random walks, distances between vertex sets, and isoperimetric numbers, are also considered.