两类八点图的图设计

Graph Design with Eight Vertices

设λKv为完全多重图,G为有限简单图,图设计G-GDλ(v)是一个序偶(X,B),其中,X是Kv的顶点集,区组集B为λKv的一种分拆,B是与G同构的子图,利用"差方法"、"带洞图设计"等工具,结合小阶数的设计,对两类八点八边图的图设计进行讨论,并确定了对任意λ的存在谱。

Let λKv be a complete multiple graph with v vertices ,and G be a finite simple graph. Graph design G-GDλ （v） is a pair of （X;β） ,in which X is the vertex set of Kv and βis a partition of all the edges in λKv, and each member of β is isomorphic to G. By means of ＂diference method＂ and ＂holey graph design＂, graph design for a graph G with eight vertices and eight edges is discussed, and the existence spectrum for the G-GDλ（v） of λKv is determined.