Containing Four Laps Of A Five-point, Five-sided Design, To The Diagram In Figure

Let K_v be a complete directed graph with v vertices, G be a simple directed subgraph without isolate vertices. A G-design of K_v, denoted by (v, k, 1)-G-GD(where k denotes the number of vertices of G, and v denotes the number of vertices of K_v), is a pair (X, B), where X is the vetice set of K_v, and B is the collection of subgraphs (called blocks) of K_v, such that each block is isomorphic to G, and any edge in K_v occurs in exactly one sugraph. In this article,the author mainly discuss the existence of graph design of ten non-isomorphic simple graphs with five vertices, five edges and a four-cycle.