Upper bounds of the second largest eigenvalue of graphs

Zhiwen Wang, Zihao Geng, Ji-Ming Guo

Let ${\lambda }_i(G)$ denote the $i$-th largest eigenvalue of adjacency matrix of a graph $G$. Gerschgorin's Theorem indicates ${\lambda }_1(G)$ belongs to the largest disk, i.e., ${\lambda }_1(G)\le {\Delta }_1(G)$,…