Graph operations that are good for greedoids

S is a local maximum stable set of a graph G, and we write S ε ψ, if the set S is a maximum stable set of the subgraph induced by S [N(S) , where N(S) is the neighborhood of S. In Levit and Mandrescu (2002) [5] we have proved that ψ is a greedoid for every forest G. The cases of bipartite graphs and triangle-free graphs were analyzed in Levit and Mandrescu (2003) [6] and Levit and Mandrescu (2007) [7] respectively. In this paper we give necessary and sufficient conditions for ψ 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; (c) the corona X o{H₁; H₂; ⋯ Hn} obtained by joining each vertex x of a graph X to all the vertices of a graph Hx.