Inspired by a famous characterization of perfect graphs due to Lovász, we define a graph G to be sum-perfect if for every induced subgraph H of G, α(H)+ω(H)|V(H)|. (Here α and ω denote the stability number and clique number, respectively.) We give a set of 27 graphs and we prove that a graph G is sum-perfect if and only if G does not contain any of the graphs in the set as an induced subgraph.