On fan-saturated graphs

Given a graph H, we say that a graph G is H-saturated if it does not contain H as a subgraph, but the addition of any edge e 6∈ E(G) results in at least one copy of H as a subgraph. Let Ft be the graph consisting of t edge-disjoint triangles that intersect at a single vertex v. We investigate the set of all m such that there exists an n vertex, m edge Ft-saturated graph, for t ≥ 2. This set is called the saturation spectrum of Ft.