# spectrum

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

Author(s):

\begin{problem} Are almost all graphs uniquely determined by the spectrum of their adjacency matrix? \end{problem}

Keywords: cospectral; graph invariant; spectrum

## The sum of the two largest eigenvalues ★★

Author(s): Gernert

\begin{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 $\lambda_1 + \lambda_2 \le n$? \end{problem}

Keywords: eigenvalues; spectrum