ELA, Volume 15, pp. 337-344, December 2006, abstract.

Limit Points for Normalized Laplacian Eigenvalues

Steve Kirkland

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.