Developments in the theory of graph spectra

Some of the main directions and newer results in the theory of graph spectra are reviewed. Some areas discussed are (i) the application of root systems to the theory of graph spectra, (ii) results concerning spectral characterizations of graphs with least eigenvalue-2, (iii) a description of some new graph invariants based on the eigenvectors of the adjacency matrix, along with (iv) the algebraic solution of the Shannon capacity problem, (v) results on spectra of random graphs, and (vi) a review of some graph polynomials related to the characteristic polynomial. Finally, (vii) a discussion of recent results concerning the spectra of infinite graphs is given.

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