A vertex subset \(S \subseteq V(G)\) is called a dissociation set of a graph G if \(\Delta (G[S])\le 1\) . A dissociation set S of G is maximal if it is not a proper subset of any other dissociation set of G. Let \(\phi (G)\) be the number of maximal dissociation sets in G. Zhang, Qian, and Huang (2024) proved that for any tree T of order n, , and characterized all trees T with . In this paper, we further study the number of maximal dissociation sets for unicyclic graphs, and prove that for any unicyclic graph U of order n, \(\phi (U)\ge \left\lfloor \frac{n}{2}\right\rfloor +2\) . Moreover, all unicyclic graphs U with \(\phi (U)= \left\lfloor \frac{n}{2}\right\rfloor +2\) are completely characterized.
