MORE ON GRAPHS WITH JUST THREE DISTINCT EIGENVALUES.

Let G be a connected non-regular non-bipartite graph whose adjacency ma- trix has spectrum ρ, μ(k); λ(l), where k, l ∊ IN and ρ > μ > λ. We show that if μ is non-main then δ(G) ≥1 + μ - λ λ, with equality if and only if G is of one of three types, derived from a strongly regular graph, a symmetric design or a quasi-symmetric design (with appropriate parameters in each case). [ABSTRACT FROM AUTHOR]