This volume continues a series of monographs in algebraic graph theory that specialize to spectral graph theory — the study of interconnections between the properties of a graph and the eigen-values and eigenvectors of the associated adja-cency matrix. The common thread between the two previous works, Spectra of Graphs — Theory and Applications [3] and Recent Results in the Theory of Graph Spec...

Content based music retrieval opens up large collections, both for the general public and music scholars. It basically enables the user to find (groups of) similar melodies, thus facilitating musicological research of many kinds. We present a graph spectral approach, new to the music retrieval field, in which melodies are represented as graphs, based on the intervals between the notes they are ...

At some time, in the childhood of spectral graph theory, it was conjectured that non-isomorphic graphs have different spectra, i.e. that graphs are characterized by their spectra. Very quickly this conjecture was refuted and numerous examples and families of non-isomorphic graphs with the same spectrum (cospectral graphs) were found. Still some graphs are characterized by their spectra and seve...

Spectral Graph Theory is the study of the spectra of certain matrices defined from a given graph, including the adjacency matrix, the Laplacian matrix and other related matrices. Graph spectra have been studied extensively for more than fifty years. In the last fifteen years, interest has developed in the study of generalized Laplacian matrices of a graph, that is, real symmetric matrices with ...

Spectral Graph Theory is the study of the spectra of certain matrices defined from a given graph, including the adjacency matrix, the Laplacian matrix and other related matrices. Graph spectra have been studied extensively for more than fifty years. In the last fifteen years, interest has developed in the study of generalized Laplacian matrices of a graph, that is, real symmetric matrices with ...

In this first talk we will introduce three of the most commonly used types of matrices in spectral graph theory. They are the adjacency matrix, the combinatorial Laplacian, and the normalized Laplacian. We also will give some simple examples of how the spectrum can be used for each of these types.

Let (G) and min (G) be the largest and smallest eigenvalues of the adjacency matrix of a graph G. Our main results are: (i) If H is a proper subgraph of a connected graph G of order n and diameter D; then (G) (H) > 1 2D (G)n : (ii) If G is a connected nonbipartite graph of order n and diameter D, then (G) + min (G) > 2 2D (G)n : These bounds have the correct order of magnitude for large and D. ...