  In a graph $G$, a subset of vertices is a dissociation set if it induces a
subgraph with vertex degree at most 1. A maximum dissociation set is a
dissociation set of maximum cardinality. The dissociation number of $G$,
denoted by $\psi(G)$, is the cardinality of a maximum dissociation set of $G$.
Extremal problems involving counting the number of a given type of substructure
in a graph have been a hot topic of study in extremal graph theory throughout
the last few decades. In this paper, we determine the maximum number of maximum
dissociation sets in a tree with prescribed dissociation number and the
extremal trees achieving this maximum value.
