Linquan Tan

Tight lower bound for the spectral radius of connected graphs with given matching number

Let $\mathscr{G}_{n,k}$ denote the family of all connected graphs of order $n$ with matching number $k$. Liu, Lou, and Trevisan~(Linear Algebra Appl., 2026) posed the following problem: Determine the spectrally minimal graphs in $\mathscr{G}_{n,k}$. In this paper we prove that for every graph $G \in \mathscr{G}_{n,k}$,...