Eigenvalues and chromatic number of a signed graph

For a signed graph Sigma, let chi(Sigma), lambda(1) and lambda(n) be the chromatic number, the maximum eigenvalue and the minimum eigenvalue of Sigma, respectively. This paper proves that, for any nonempty signed graph Sigma with n vertices, chi(Sigma) >= max {1 + lambda(1)/vertical bar lambda(n)vertical bar, n/n - lambda(1)}. These two bounds extend the classical spectral lower bounds of Hoffman and Cvetkovic for an ordinary graph, respectively. (C) 2021 Elsevier Inc. All rights reserved.