价k_i（i≠0）均为2的交换结合Scheme

COMMUTATIVE ASSOCIATION SCHEMES WITH ALL VALENCIES k_i=2(i≠0)

价是交换结合Ｓｃｈｅｍｅ的重要数量特征，有较强的组合性质，利用价来讨论某些交换结合Ｓｃｈｅｍｅ的构造与性质，是一个常用的方法．设＝（Ｘ，｛Ｒｉ｝ｉ＝０，１，．．．，ｄ）是一个类ｄ的交换结合Ｓｃｈｅｍｅ．ｋ０，ｋ１，．．．，ｋｄ是的价．本文证明了，若ｋ１＝ｋ２＝．．．＝ｋｄ＝２，则 是对称结合Ｓｃｈｅｍｅ．

Valencies are important parameters of commutative association schemes which have strong combinatorical properties,and it is usual to make use of valencies to study the structure and properties of commutative association schemes.Let =(X,R,i=0,1,....d) be a commutative association scheme with class d.and k0,k1,...,kd be valencies of.In this paper we have proved that if k1=k2=...=kd=2,is symmetric.