The Meta(H＞T, λ) For All Available T(?)H(?)K₄ And Any λ

Let H be a finite simple graph, T be a sub-graph of H. A graph designλK_v(?) H is a pair (V,β), where V is the vertex-set of K_v,βis a family of subgraphs isomorphic to H, such that each edge in K_v appears in exactlyλblocks ofβ. Now, partition each B∈B into B' and B\B', where B' is isomorphic to T. If the edges in D(H\T) = {B\B' : B∈β] can be rearranged as a union D(T) of T-copies, then (V,β(T)∪D(T)) forms a graph designλK_v(?)T, whereβ(T) = {B' : B∈β}. The procedure fromλK_v(?)H toλK_V(?)T is called a metamorphosis of the (V,β), denoted by (H > T)-GM_λ(v).The existence spectrum of (H > T)-GM_λ(v) is denoted by Meta(H > T,λ) = {v : (?)(H > T)-GM_λ(v)}. In this thesis, for all available T (?) H (?) K₄ and any A, the correspondingspectrums Meta(H > T,λ) are completely determined.