Upper bounds of the second largest eigenvalue of graphs

Zhiwen Wang, Zihao Geng, Ji-Ming Guo

Let $\hat{I}{»}_i(G)$ denote the $i$-th largest eigenvalue of adjacency matrix of a graph $G$. Gerschgorin's Theorem indicates $\hat{I}{»}_1(G)$ belongs to the largest disk, i.e., $λ_1(G)\leΔ_1(…