Graph operations that are good for greedoids

SS is a local maximum stable set   of a graph GG, and we write S∈Ψ(G)S∈Ψ(G), if the set SS is a maximum stable set of the subgraph induced by S∪N(S)S∪N(S), where N(S)N(S) is the neighborhood of SS. In Levit and Mandrescu (2002) [5] we have proved that Ψ(G)Ψ(G) is a greedoid for every forest GG. 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(G)Ψ(G) to form a greedoid, where GG is: (a)the disjoint union of a family of graphs;(b)the Zykov sum of a family of graphs;(c)the corona X∘{H1,H2,…,Hn}X∘{H1,H2,…,Hn} obtained by joining each vertex xx of a graph XX to all the vertices of a graph HxHx.