The domination number \(\gamma(G)\) and the irredundance number \(ir(G)\) of a graph \(G\) have been considered by many authors. It is well known that \(ir(G) \leq \gamma(G)\) holds for all graphs \(G\). In this paper we determine all pairs of connected graphs \((X, Y)\) such that every graph \(G\) containing neither \(X\) nor \(Y\) as an induced subgraph satisfies \(ir(G) = \gamma(G)\).