Association schemes
Association schemes
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DOI：
10.1007/978-3-642-74341-2_2
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发表时间：
1996-03
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本章第一部分简要介绍了(对称)结合方案的基本理论。这类方案实质上是将一个完整图分割成以特定方式相互关联的正则子图。更广泛的治疗，见Bannai&Ito[33]。本章的最后部分讨论了一些特殊的主题。虽然我们将独立于本章的结果发展距离正则图的大部分理论，但我们将在更专门的主题中使用关于结合方案的概念和结果，例如，q-多项式排序(第8章)和图中的码(第11章)。重数公式(2.2.2)和界(2.3.3)以及Krein条件(2.3.2)将在第四章中用于距离正则图。
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.