On limit points of Laplacian spectral radii of graphs Original Research Article

The study of limit points of eigenvalues of adjacency matrices of graphs was initiated by Hoffman [A.J. Hoffman, On limit points of spectral radii of non-negative symmetric integral matrices, in: Y. Alavi et al. (Eds.), Lecture Notes Math., vol. 303, Springer-Verlag, Berlin, Heidelberg, New York, 1972, pp. 165–172]. There he described all of the limit points of the largest eigenvalue of adjacency matrices of graphs that are no more than image. In this paper, we investigate limit points of Laplacian spectral radii of graphs. The result is obtained: Let image, β0=1 and image be the largest positive root ofimageLet image. Then4=α0<α1<α2