Graphs with Diameter $n-e$ Minimizing the Spectral Radius

Jingfen Lan, Linyuan Lu, Lingsheng Shi

The spectral radius $\rho (G)$ of a graph $G$ is the largest eigenvalue of its adjacency matrix $A(G)$. For a fixed integer $e\ge 1$, let $G_{n,n-e}^{min}$ be a graph with minimal spec…