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
Graph Designs for Two Kinds of Graphs with 8 Vertices and 8 Edges
摘要/Abstract
摘要：
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.
Abstract：
Let λKv be the complete multigraph of order v and index λ,G be a finite simple graph.A G-design 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 λKv (called blocks),such that each block is isomorphic to G and any two distinct vertices in Kv are 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.
关键词
Key words：
graph design
;
holey graph design
;
incomplete holey graph design
参考文献 10
- [1] BOSÀK J.Decompositions of Graphs[M].Boston:Kluwer Academic Publishers,1990.
- [2] HEINRICH K.Path-decompositions[J].Le Matematiche (Catania),1992(12):241-258.
- [3] BERMOND J C,SCHONHEIM J.G-decompositions of Kn,Where G Has Four Vertices or Less[J].Discrete Mathematics,1977(19):113-120.
- [4] BERMOND J C,HUANG C,ROSA A,et al.Decomposition of Complete Graphs into Isomorphic Subgraphs with Five Vertices[J].Ars Combinatoria,1980(10):211-254.
- [5] YIN Jianxing,GONG Busheng.Existence of G-designs with |V(G)|=6[J].Combinatorial Designs and Application,1998,126:201-218.
- [6] KANG Qingde,DU Yanke,TIAN Zihong.Docomposition of λKv into Some Graph with Six Vertices and Seven Edges[J].Journal of Statistical Planning and Inference,2006,136:1394-1409.
- [7] 高印芝,左会娟,刘义芬.几类7点7边图的图设计与最优填充[J].河北师范大学学报:自然科学版,2003,27(2):123-126.
- [8] 高印芝,左会娟,康庆德.含偶长圈的7点7边图的图设计[J].应用数学学报,2004,27:646-658.
- [9] 张艳芳,梁志和.拟群在构作图Km+2\Km的图设计中的应用[J].江西师范大学学报:自然科学版,2008,32:579-581.
- [10] 李明超,康庆德,霍京京.完全图Kv的8长圈最大填充设计[J].河北师范大学学报:自然科学版,2009,33(4):421-424.