Strongly Regular Graphs Derived from Combinatorial Designs
Strongly Regular Graphs Derived from Combinatorial Designs
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由组合设计得出的强正则图
DOI：
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发表时间：
1970
期刊：
影响因子：
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通讯作者：
J. Seidel
中科院分区：
文献类型：
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作者：
J. Goethals;J. Seidel
离散数学中的几个概念，例如分块设计、拉丁方、哈达玛矩阵、战术配置、纠错码、几何配置、有限群和图，绝不是独立的。这些概念的组合可能有助于其中任何一个概念的发展，有时还揭示出隐藏的相互关系。在本文中，强正则图的概念在这方面发挥着核心作用，下面回顾其定义。在第 2 节中，给出了图的纤维型构造，将其应用于 λ = 1 和 Hadamard 矩阵的分块设计，产生强正则图。该方法虽然其应用仍然受到限制，但可能有助于进一步发展。在第 3 节中，我们处理块设计，首先由 Shrikhande [22] 考虑，其中任何块对的交集中的点数仅达到两个值。
Several concepts in discrete mathematics such as block designs, Latin squares, Hadamard matrices, tactical configurations, errorcorrecting codes, geometric configurations, finite groups, and graphs are by no means independent. Combinations of these notions may serve the development of any one of them, and sometimes reveal hidden interrelations. In the present paper a central role in this respect is played by the notion of strongly regular graph, the definition of which is recalled below. In § 2, a fibre-type construction for graphs is given which, applied to block designs with λ = 1 and Hadamard matrices, yields strongly regular graphs. The method, although still limited in its applications, may serve further developments. In § 3 we deal with block designs, first considered by Shrikhande [22], in which the number of points in the intersection of any pair of blocks attains only two values.