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±¨¸æÕªÒª£ºIn this talk we first introduce the problems on the characterization of the graphs with distinct eigenvalues, posed by F. Harary et al in 1974, and the graphs with k's main eigenvalues, posed by Cvetkovic et al in 1997. Then we review the main results in this subject. Finally, we report some of our recent works on the characterization of the graphs with distinct eigenvalues and main eigenvalues.
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