| Let K_v be a complete dircted graph with v vertices, G be a simple directedsubgraph. A G-design of K_v, denoted by (v, k, 1)-GD, is apair (X, (?)), where X isthe vertice set of K_v, and (?) is the collection of subgraphs (called blocks) of K_V, suchthat each block is ismorphic to G, and any edge in K_v occurs in exactly one subgraph.In this article, the anthor study the existence of graph design of non-isomorphic simpledirectedθgraphs with six vertices, and eight non-isomorphic simple directedθgraphswith seven vertices and directed cycle. |