Given a graph $G$ with $S \subseteq V_G$, we call $S$ a maximum dissociation set if the induced subgraph $G[S]$ contains no path of order $3$, and subject to this condition, the subset $S$ has the maximum cardinality. The dissociation number of $G$ is the cardinality of a maximum dissociation set. Inspired by the results of [26, 27] on the maximal number of maximum dissociation sets, in this contribution we investigate the maximal number of maximum dissociation sets in forests with fixed order and dissociation number. Firstly, a lower bound on the dissociation number of a forest with fixed ord...
