On the distribution of the maximum eigenvalue of graphs

Given a graph G, let λ (G) denote the largest eigenvalue of the adjacency matrix of G. We prove that for any λ ≥ 2+ 5 ( = 2.058+) there exists a sequence of graphs G1,G2,... such that limk→∞λ(Gk) = λ, thus answering a question posed by Hoffman. © 1989.