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.