Abstract
Let denote the number of Laplacian eigenvalues of a graph G in an interval I and let denote the independence number of G. In this paper, we determine the classes of graphs that satisfy the condition when and , where n is the order of G. When , for some . When , there are two types of graphs and of order n = p + q + r + 2, which we call the binary star graphs. Also, we show that the binary star graphs with p = r are determined by their Laplacian spectra.
Disclosure statement
No potential conflict of interest was reported by the authors.