Interlacing properties of Laplacian eigenvalues of chain graphs

Abstract

Chain graphs are {2K<inf>2</inf>,C<inf>3</inf>,C<inf>5</inf>}-free graphs. The Laplacian spectrum of a chain graph of order n consists of n−2h integer eigenvalues and 2h possibly non-integer eigenvalues that correspond to the associated quotient matrix of order 2h. We show that 2h complementary eigenvalues interlace vertex degrees. As an application, we confirm that the Brouwer's conjecture holds for chain graphs.