具有固定价的结合概型：（Ⅰ）  

ON ASSOCIATION SCHEMES WITH FIXED VALENCY

作　　者：徐邦腾[1] 

机构地区：[1]湖北大学

出　　处：《数学杂志》1996年第1期39-46,共8页Journal of Mathematics

摘　　要：结合概型的分类，是件十分重要而又非常困难的工作。在结合概型中，价是很重要的参数，有较强的组合意义。利用价来给出某些结合概型的分类，是一个常用的方法。设是一个类ｄ的结合概型，Ａ０，Ａ１，…，Ａｄ和ｋ０，ｋ１，…，ｋｄ分别是的邻接矩阵和价，且ｋ１＝ｋ２＝…＝ｋｄ＞２．本文证明了，若某个Гｉ＝（Ｘ，Ｒｉ）是无向连通图且ｖ（ｉ２）≤２ｖ（Ａｉ），１≤ｉ≤ｄ，则ｄ＝１，即是平凡的结合概型．The classification of association schemes is very important and extremely difficult. In association schemes,valencies are important parameters which have strong combinatorical properties.It is usual to make use of the valencies to classify some association schemes.Let be an association scheme with class d,and A0,A1,…,Ad and k0,k1 …,kd be adjacency matrices and valencies of,respectively. Assume that k1=k2=…=kd>2.In this paper we have proved that if Гi= (X,Ri) is an undirected connected graph and for some i,1≤i≤d,then d=1,i. e.is trivial.

关 键 词：结合概型 邻接矩阵 价 组合论 距离正则图 

分 类 号：O157[理学—数学]