On spectral Turán theorems: confirming a conjecture of Guiduli and two problems of Nikiforov

Lele Liu, Bo Ning

Let $G$ be an $n$-vertex graph, and let $\hat{I}»(G)$ and $\hat{I}{»}_n(G)$ denote the largest and smallest eigenvalues of its adjacency matrix. Write $e(G)$ for the number of edges of $G$, $d(G…