2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/75975We derive bounds on the size of an independent set based on eigenvalues. This generalizes a result due to Delsarte and Hoffman. We use this to obtain new bounds on the independence number of the Erdős-Rényi graphs. We investigate further properties of our bounds, and show how our results on the Erdős-Rényi graphs can be extended to other polarity graphs.18 pagesCombinatorics05C69; 51E15, 51E12text