# Gernert, Dieter

## 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