Spin Models on Bipartite Distance-Regular Graphs
Spin Models on Bipartite Distance-Regular Graphs
复制标题
二分距离正则图上的自旋模型
DOI：
10.1006/jctb.1995.1037
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发表时间：
1995
期刊：
影响因子：
--
通讯作者：
K. Nomura
中科院分区：
文献类型：
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作者：
K. Nomura
自旋模型是由V.Jones(Pac.J.Math.137(1989)，311-336)来构造纽结和链环的不变量。自旋模型定义为满足几个公理的有限集X和X×X上的函数w的对S=(X，w)。在距离正则图Γ=(X，E)上，只要满足w(a，b)=tΓ(a，b)，就可以构造出一些重要的自旋模型，其复数为t0，t1，…，Td(d为∂的直径)。本文确定了以这种方式给出具有不同T1，…，Td自旋模型的二部距离正则图，证明了这样的二部距离正则图满足一个强正则条件(它是2-齐次的)，并对满足这个正则性条件的二部距离正则图进行了分类。
Spin models were introduced by V. Jones (Pac. J. Math.137 (1989), 311-336) to construct invariants of knots and links. A spin model will be defined as a pair S = (X, w) of a finite set X and a function w on X × X satisfying several axioms. Some important spin models can be constructed on a distance-regular graph Γ = (X, E) with suitable complex numbers t0, t1, ..., td (d is the diameter of Γ) by putting w(a, b) = t∂(a, b). In this paper we determine bipartite distance-regular graphs which give spin models in this way with distinct t1, ..., td We show that such a bipartite distance-regular graph satisfies a strong regularity condition (it is 2-homogeneous), and we classify bipartite distance-regular graphs which satisfy this regularity condition.