\(R\)-annihilated and independent perfect neighborhood sets in chordal graphs (Q1974533)

Let \(\theta_i(G)\), \(\text{ra}(G)\) be the minimum cardinality of an independent perfect neighborhood set and an \(R\)-annihilated set, respectively. In 1999, Favaron and the author showed that the difference \(\theta_i(G)- \text{ra}(G)\) can be arbitrarily large; see \textit{O. Favaron} and \textit{J. Puech} [Discrete Math. 197/198, 269-284 (1999; Zbl 0957.05081)]. In the present paper, the author shows that the inequality \(\theta_i(G)\leq \text{ra}(G)\) holds for chordal graphs and for \(C_{1,2,2}\)-free graphs.