Sharp spectral lower bounds for the booksize of a graph

Let $G$ be an $n$-vertex graph with $e(G)$ edges, and let $λ(G)$ denote the largest eigenvalue of its adjacency matrix. The booksize $\mathrm{bk} (G)$ of $G$ is defined as the largest number of triangles sharing a common edge. The main purpose of this note is to prove that if $λ(G)\geqλ(T_{n,2})$ an