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Graph Theory

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

Author(s):

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

Keywords: cospectral; graph invariant; spectrum

Posted by mdevos
updated March 26th, 2013
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Graph Theory » Algebraic G.T.

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

Posted by mdevos
updated January 13th, 2009
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