The limit points of Laplacian spectra of graphs

Abstract 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, α ( G )>0, if and only if G is connected. This observation let Fiedler to call α ( 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.