Laplacian energy of graphs and digraphs.

Spectral graph theory (Algebraic graph theory) which emerged in 1950s and 1960s is the study of properties of a graph in relationship to the characteristic polynomial, eigenvalues and eigenvectors of matrices associated to the graph. The major source of research in spectral graph theory has been the study of relationship between the structural and spectral properties of graphs. Another source has research in quantum chemistry. Just as astronomers study stellar spectra to determine the make-up of distant stars, one of the main goals in spectral graph theory is to deduce the principal properties and structure of a graph from its graph spectrum (or from a short list of easily computable invariants). The spectral approach for general graphs is a step in this direction.Digital copy of Thesis.University of Kashmir