Variants of spectral Turán theorems and eigenvectors of graphs

Lele Liu, Bo Ning

In 2002, Nikiforov proved that for an $n$-vertex graph $G$ with clique number $\omega$ and edge number $m$, the spectral radius $\lambda (G)$ satisfies $\lambda (G)\le \sqrt{2(1-1/\omega )m}$, which c…