  S is a local maximum stable set of a graph G, if the set S is a maximum
stable set of the subgraph induced by its closed neighborhood. In (Levit,
Mandrescu, 2002) we have proved that the family of all local maximum stable
sets is a greedoid for every forest. The cases of bipartite graphs and
triangle-free graphs were analyzed in (Levit, Mandrescu, 2004) and (Levit,
Mandrescu, 2007), respectively. In this paper we give necessary and sufficient
conditions for the family of all local maximum stable sets of a graph G to form
a greedoid, where G is: (a) the disjoint union of a family of graphs; (b) the
Zykov sum of a family of graphs, or (c) the corona X*{H_1,H_2,...,H_n} obtained
by joining each vertex k of a graph X to all the vertices of a graph H_k.
