Sharif Digital Repository

In this thesis we investigate the spectrum of the Laplacian matrix of a graph. Although its use dates back to Kirchhoff, most of the major results are much more recent. The first chapter of this thesis is devoted to the integral Laplacian eigenvalues of graphs. In Section 2, particular attention is given to multiplicities of integer eigenvalues and to the effect on the spectrum of various modifications. In Section 3, the Laplacian integral graphs are investigated. The Section 4 relates the degree sequence and the Laplacian spectrum through majorization.The second chapter presents the result on permanent of the Laplacian matrix of graphs and permanental roots. In Section 2, we investigate...