A note on the

For any graph G, a subset D ⊆ V (G) is called a P3-isolating set of G if G − N[D] contains no P3 as a subgraph, that is, consists of isolated vertices and isolated edges only. The P3-isolation number of G, denoted by ι(G, P3), is the cardinality of a smallest P3-isolating set of G. Zhang and Wu [Discrete Appl. Math. 304 (2021) 365–374] investigated the parameter ι(G, P3) of a graph, and they proved that if G ∉ {P3, C3, C6} is a connected graph of order n, then $ \iota{(G,P_3)}\leq\frac27n$. In this paper, we shall prove that if G ∉ {P3, C7, C11} is a connected graph of order n without triangles and induced 6-cycles, then $ \iota{(G,P_3)}\leq\frac n4$, and the upper bound is sharp. This extends a result on ι(T, P3) of a tree T by Caro and Hansberg [Filomat 31 (2017) 3925–3944].