Optimal Embeddings of Distance Regular Graphs into Euclidean Spaces

Details Optimal Embeddings of Distance Regular Graphs into Euclidean Spaces Optimal Embeddings of Distance Regular Graphs into Euclidean Spaces

2005-09-30

arxiv.org/abs/math/0509716v3

J. Combin. Theory Ser. B 98 (2008), 95-104

Mathematics

Combinatorics

10 pages, (v3) some corrections, accepted in Journal of Combinatorial Theory, Series B

Scientific paper

10.1016/j.jctb.2007.06.002

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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