Are almost all graphs determined by their spectrum? ★★★


Problem   Are almost all graphs uniquely determined by the spectrum of their adjacency matrix?

Keywords: cospectral; graph invariant; spectrum

The sum of the two largest eigenvalues ★★

Author(s): Gernert

Problem   Let $ G $ be a graph on $ n $ vertices and let $ \lambda_1 \ge \lambda_2 \ge \ldots \ge \lambda_n $ be the eigenvalues of $ G $. Is $ \lambda_1 + \lambda_2 \le n $?

Keywords: eigenvalues; spectrum

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