七点有向θ图的图设计

Graph design of directed θ graphs with seven vertices

设Kv是一个v点的有向完全图,G是一个简单有向图,Kv的一个G-设计,记为(v,G,1)-GD,是指一个二元组(X,B),其中X为Kv的点集,B为Kv的一些子图(也称为区组)构成的集合,使得任一子图(区组)与G同构,且Kv的任意两个不同点组成的有向边恰在B的一个区组中出现。研究了七点有向图的图设计的存在性问题。

Let Kv be a complete directed graph with v vertices,G be a simple directed subgraph.A G-design of Kv,denoted by（v,G,1）-GD,is a pair（X,B）,where X is the vertices set of Kv,and B is the collection of Kv subgraphs（blocks） of Kv,such that each block is isomorphic to G,and any edge in Kv occurs in exactly one subgraph.In this article,the author study the existence of graph design of non-isomorphic simple directed graphs with seven vertices.