摘要
设λKv是λ重 v点完全图 ,G为一个无孤立点的有限简单图 .λKv的一个 G-覆盖设计 ,记为(v,G,λ) - CD,是指一个对子 (X,B) ,其中 X为点集 ,B为 λKv 的一些子图 (亦称为区组 )构成的集合 ,使得任一区组均与 G同构 ,且任意两个不同点组成的边至少在 B的 λ个区组中出现 .讨论了两类六点七边图 Gi=K2 ,3+e(i=1,2 )的最优覆盖的存在性问题 .证明了存在 (v,Gi,λ) -OCD,i=1,2 ,当且仅当 v≥ 6,除去非最优 (但为最大 )的 C(6,G1,1) =4 .
Let λK_v be the complete multigraph with v vertices, where any two distinct vertices x and y are joined by λ edges (x,y). Let G be a finite simple graph. A Gcovering design of λK_v,denoted by (v,G,λ)CD , is a pair(X,B) where X is the vertex set and B is a collection of subgraphs of K_v, called blocks, such that each block is isomorphic to G and any two distinct vertices in K_v are joined in at least λ blocks of B. In this paper, we discussed the existence of G_ioptimal covering, where G_i=K_ 2,3+e(i=1,2) has six vertices and seven edges. We have obtained the result:(v,G_i,λ)OCD,i=1,2 exist if v≥6, with the not optimal values C(6,G_i,1)=4.
出处
《兰州大学学报（自然科学版）》
CAS
CSCD
北大核心
2002年第6期6-13,共8页
Journal of Lanzhou University(Natural Sciences)
基金
河北省自然科学基金资助项目 (10 10 92 )
关键词
最优覆盖
图
设计
图覆盖
graph
graph covering
graph design
