在线阅读 --自然科学版 2003年4期《8长圈加1条弦的图设计》
8长圈加1条弦的图设计--[在线阅读]
左会娟, 康庆德
河北师范大学数学与信息科学学院, 河北石家庄 050016
起止页码: 337--341页
DOI:
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-设计记作(v,G,λ)-GD=(X,B),其中X是完全图Kv的顶点集,BKv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.

Decompositions of λKv into C_8~((r))
ZUO Hui-juan, KANG Qing-de
College of Mathematics and Information Science, Hebei Normal University, Hebei Shijiazhuang 050016, China
Abstract:
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.

收稿日期: 2002-12-19
基金项目: 河北省自然科学基金资助项目(101092)

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