The volume and foundation of star trades

An x-star trade consists of two disjoint decompositions of some simple graph H   into copies of K1,xK1,x, the graph known as the x-star. The number of vertices of H is referred to as the foundation   of the trade, while the number of copies of K1,xK1,x in each of the decompositions is called the volume of the trade. We determine all values of x  , vv and s   for which there exists a K1,xK1,x-trade of volume s   and foundation vv.