六点七边图的图设计

The design of the graphs with six points and seven edges

六点七边图(不带孤立点的简单图)共有17个图.应用GDD、加权和闭包思想给出了所有六点七边图图设计的构造方法,同时在构造G-HD(7k)(k=3,4,5,6,8)时运用了阿贝尔群的性质,简化了构造过程,并用此方法举例说明如何具体讨论六点七边图图设计的存在性问题,从而得出如下结论:满足v≥k,v(v-1)≡0(mod2e),v-1≡0(modd)且v≥14时,均存在(v,G,1)-GD,其中对v=7,v=8的情况单独讨论.

There are seventeen graphs and each graph has six vertices and seven edges. The author attempts to introduce graph design method of the graphs with six vertices and seven edges by applying GDD, weight and B(K) to the paper. At the same time the author exerts the feature of Abel group to make G-HD(7~k), k=3,4,5,6,8. So the course is simplified.In the paper the author makes an example in order to illustrate the method. Consequently the central conclusion obtained is that the graph design (v,G,1)-GD exists when the graphs satisfy v≥k, v (v-1)≡0 (mod()2e), v-1≡0 (mod()d) and v≥14, on the side the graph designs are separately discussed when v=7, v=8.