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Given a simple graph $G$, a subset $S\subseteq V(G)$ is an independent $[1,2]$-set if no two vertices in  $S$ are adjacent and for every vertex $v\in V(G) \backslash S, 1\leq |N(v) \cap S| \leq 2$, that is, every vertex $v\in V(G) \backslash S$ is adjacent to at least one but not more than two vertices in $S$. This paper investigates the existence of independent $[1,2]$-sets of some families of graphs, namely, Path $P_n$, Cycle $C_n$, Complete Graph $K_n$, Star $S_n$, Fan $F_n$, Wheel $W_n$, Complete Bipartite $K_{m,n}$, Windmill $K_n^{(m)}$, Helm $H_n$, Flower $Fl_n$, Comb $P_n \odot K_1$, and Crown $C_n \odot K_1$.

Independent $[1,2]$-set; Windmill $K_n^{(m)}$; Helm $H_n$; Flower $Fl_n$