  Given a graph G, a subset of vertices is called a maximum dissociation set if
it induces a subgraph of maximum degree at most 1 and the subset has maximum
cardinality. In this paper, we first characterize the set of vertices of a tree
that are contained in all, or in no, maximum dissociation sets of the tree.
Then we present a linear time recognition algorithm which can determine whether
a given vertex in a tree is in all (or no) maximum dissociation sets of the
tree. Thus we can find all vertices contained in all (or no) maximum
dissociation sets of a tree of order n in O(n2) time.
