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spectrum
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
The sum of the two largest eigenvalues ★★
Author(s): Gernert
Problem Let
be a graph on
vertices and let
be the eigenvalues of
. Is
?
![$ G $](/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png)
![$ n $](/files/tex/ec63d7020a64c039d5f6703b8fa3ab7393358b5b.png)
![$ \lambda_1 \ge \lambda_2 \ge \ldots \ge \lambda_n $](/files/tex/4dab458778057be2d191e80cde57ee36191958e9.png)
![$ G $](/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png)
![$ \lambda_1 + \lambda_2 \le n $](/files/tex/a383bcff06b594eb75570de2cd8813be94854126.png)
Keywords: eigenvalues; spectrum
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