The Exact Maximum of the Spectral Sum of Graphs

Jing Huang, Wei Wei

For a simple graph $G$ of order $n$, let $S_2(G)={\lambda }_1(G)+{\lambda }_2(G)$ denote its spectral sum. We determine, for every $n\ge 5$, the exact maximum of $S_2(G)$ and all equality cases. The…