距离正则图在欧几里得空间中的最优嵌入

Optimal Embeddings of Distance Regular Graphs into Euclidean Spaces

Frank Vallentin

备注：: 10 pages, (v3) some corrections, accepted in Journal of Combinatorial Theory, Series B
发表信息：: J. Combin. Theory Ser. B 98 (2008), 95-104
DOI：: 10.1016/j.jctb.2007.06.002

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摘要：

本文给出了距离正则图在欧几里得空间中的最小失真嵌入的一个下界。我们使用下界来寻找汉明图、约翰逊图和所有强正则图的最小失真。我们的技术涉及半定规划和利用最优化问题的代数结构，使找到最小失真的下界的问题减少到一个关于正交多项式的分析问题。

英文摘要：

In this paper we give a lower bound for the least distortion embedding of a distance regular graph into Euclidean space. We use the lower bound for finding the least distortion for Hamming graphs, Johnson graphs, and all strongly regular graphs. Our technique involves semidefinite programming and exploiting the algebra structure of the optimization problem so that the question of finding a lower bound of the least distortion is reduced to an analytic question about orthogonal polynomials.

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