Graphs characterized by the second eigenvalue

Abstract

Abstract In this paper we prove that for a simple graph G without isolated vertices 0 < λ 2 ( G ) < 1/3 if and only if G ≅ K̄ n ‐3 V ( K 1 ∪ K 2 ), the graph obtained by joining each vertex of K̄ n ‐3 to each vertex of K 1 ∪ K 2 ). © 1993 John Wiley & Sons, Inc.