The limit points of Laplacian spectra of graphs

Let G be a graph on n vertices. Denote by L(G) the Laplacian matrix of G. It is easy to see that L(G) is positive semidefinite symmetric and that its second smallest eigenvalue, alpha(G) > 0, if and only if G is connected. This observation let Fiedler to call alpha(G) the algebraic connectivity of the graph G. In this paper, the limit points of Laplacian spectra of graphs are investigated. Particular attention is given to the limit points of algebraic connectivity. Some new results and generalizations are included. (C) 2002 Elsevier Science Inc. All rights reserved.