【摘要】 设λKv 是λ重v点完全图 ,G是无孤立点的有限简单图 .将G设计 (G填充 )记作 (v ,G ,λ)GD( (v ,G ,λ)PD)是指一个序偶 (X ,B) ,其中X是完全图Kv 的顶点集 ,B是Kv 中同构于G的子图 (区组 )的集合 ,使得Kv 中每条边恰好 (至多 )出现在B的λ个区组中 .讨论了 3类 7点 7边图Gi(i=1,2 ,3)的图设计及最优填充问题 ,并给出了 (v ,Gi,1)GD及 (v ,Gi,1)OPD (i=1,2 ,3)存在的谱 .更多还原

【Abstract】 Let λK v be the complete multigraph with v vertices,G be a finite simple graph.A Gdesign(Gpacking design) of λK v,denoted by (v,G,λ)GD ((v,G,λ)PD) is a pair (X,B),where X is the vertex set of K v 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 exactly (at most) λ blocks of B.The G i-designs and G i-optimal packings is discussed,where G i(i=1,2,3) has seven vertices and seven edges,and solved the existence spectrum of (v,G i,1)GD and (v,G i,1)OPD,i=1,2,3.更多还原