LAUSR

Abstract Let G be a graph and I be an interval. In this paper, we present bounds for the number m G I of Laplacian eigenvalues in I in terms of structural parameters of G. In particular, we show that m G ( n − α ( G ) , n ] ≤ n − α ( G ) and m G ( n − d ( G ) + 3 , n ] ≤ n − d ( G ) − 1 , where α ( G ) and d ( G ) denote the independence number and the diameter of G, respectively. Also, we characterize bipartite graphs that satisfy m G [ 0 , 1 ) = α ( G ) . Further, in the case of triangle-free or quadrangle-free, we prove that m G ( n − 1 , n ] ≤ 1 .