Association schemes
Association schemes
复制标题
DOI：
10.1007/978-1-4614-1939-6_11
复制
发表时间：
1996-03
期刊：
影响因子：
--
通讯作者：
Andries E. Brouwer;W. Haemers
中科院分区：
文献类型：
--
作者：
Andries E. Brouwer;W. Haemers
本章第一部分简要介绍了（对称）关联方案的基本理论。此类方案本质上是将完整图划分为以特定方式相互关联的规则子图。对于更广泛的治疗，请参阅 Bannai & Ito[33]。本章的最后一部分讨论一些特殊主题。尽管我们将独立于本章的结果来发展距离正则图理论的大部分内容，但我们将使用有关关联方案的概念和结果来实现更专业的主题，例如 Q 多项式排序（第 8 章）和图中的代码（第 11 章）。重数公式 (2.2.2) 和界限 (2.3.3) 以及这里在一般上下文中开发的 Kerin 条件 (2.3.2) 将在第 4 章中的距离正则图中重复出现。
The first part of this chapter contains a short account of the basic theory of (symmetric) association schemes. Such schemes are essentially partitions of a complete graph into regular subgraphs which are interrelated in a specific way. For a more extensive treatment, see Bannai& Ito[33]. The last part of this chapter treats some special topics. Although we shall develop large parts of the theory of distance-regular graphs independently of the results of this chapter, we shall use concepts and results about association schemes for more specialized topics such as, e.g.,Q-polynomial orderings (Chapter 8) and codes in graphs (Chapter 11). Multiplicity formulas (2.2.2) and bounds (2.3.3) as well as the Krein conditions (2.3.2) developed here in general context will recur for distance-regular graphs in Chapter 4.