Minimum embedding of a into a

Let H be a subgraph of a graph G . An H -design ( U , C ) of order u and index λ is embedded into a G -design ( V , B ) of order v and index μ if λ ≤ μ , U ⊆ V and there is an injective mapping f : C → B such that B is a subgraph of f ( B ) for every B ∈ C . The mapping f is called the embedding of ( U , C ) into ( V , B ) . In this paper, we study the minimum embedding of a kite system of order u and index λ (denoted by KS ( u , λ ) ) into a kite system of order u + w and index μ .