Graphs characterized by the second eigenvalue

In this paper we prove that for a simple graph G without isolated vertices 0 < λ2(G) < 1/3 if and only if G ≅ Kn-3 V (K1 ∪ K2), the graph obtained by joining each vertex of Kn-3 to each vertex of K1 ∪ K2). © 1993 John Wiley & Sons, Inc.