两类8点8边图的图设计

Graph Designs for Two Kinds of Graphs with 8 Vertices and 8 Edges

设λKv是v阶λ重完全图,G是一个有限简单图.图设计(v,G,λ)-GD是一个有序对(X,B),其中X是完全图Kv的顶点集合,B是λKv中与G同构的子图(叫做区组)的集合,使得Kv中任意一条边恰出现在B的λ个区组中.研究了两类8点8边图Gi(i=1,2)的图设计,并给出了(v,Gi,1)-GD(i=1,2)的存在谱.

Let λKv be the complete multigraph of order vand index λ,Gbe a finite simple graph.A Gdesign of λKv,denoted by（v,G,λ）-GD,is a pair（X,B）,where Xis the vertex set of Kvand Bis a collection of subgraphs of λKv（called blocks）,such that each block is isomorphic to Gand any two distinct vertices in Kvare joined in exactly λ blocks of B.In this paper,we investigate the graph designs for two kinds of graphs with 8 vertices and 8 edges and obtain the existence spectrum of（v,Gi,1）-GD,where i=1,2.