期刊信息
- 刊名： 河北师范大学学报（自然科学版）Journal of Hebei Normal University (Natural Science)
- 主办： 河北师范大学
- ISSN： 1000-5854
- CN： 13-1061/N
- 中国科技核心期刊
- 中国期刊方阵入选期刊
- 中国高校优秀科技期刊
- 华北优秀期刊
- 河北省优秀科技期刊
Decompositions of λKv into C_8~((r))
摘要/Abstract
设λKv是λ重v点完全图,G是无孤立点的有限简单图.将G-设计记作(v,G,λ)-GD=(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中每条边恰好出现在B的λ个区组中.利用差分法、拟群及组合设计理论中经典的PBD方法等,建立了若干有效的构造图设计的递归方法,并给出了若干小设计的直接构造.最终解决了λ=1时,8长圈加1条弦的图设计的存在性问题,并给出其λ=1时的存在谱.
Let λKv be the complete multigraph with v vertices, G be a finite simple graph.A G-decomposition of λKv,denoted by (v,G,λ)-GD is a pair (X,B),where X is the vertex set of Kv and B is a collection of subgraphs of Kv,such that each subgraph is isomorphic to G and any edge in Kv appear in exact λ subgraphs of B.By difference,quasi group and the dassical PBD method of combinatorial design theory,many effective recursive methods of graph design have been formed and some direct constructure of small number design are given.Eventually,the existence of (v,C8(r),1)-GD has been completely solved and the existence spectrum is given.