Lower bounds on the spectra of symmetric matrices with nonnegative entries (Q1070312)

Let G be a simple graph on v vertices and A(G) its adjacency matrix. Let \(\lambda_ 1(G)\leq...\leq \lambda_ v(G)\) be the eigenvalues of A(G). This paper deals with the problem of finding sharp lower bounds for \(\lambda_ 1(G)\). As an example we mention the result stating that if \(v=2n\), then \(\lambda_ 1(G)\geq -n\) and is equal to -n if and only if G is isomorphic to the graph \(K_{n,n}\). A similar result is proved for \(v=2n+1\). The paper ends with bounds for the minimal eigenvalue of a symmetric nonnegative matrix.