The rank of connection matrices and the dimension of graph algebras

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Abstract

Connection matrices were introduced in [M. Freedman, L. Lovász, A. Schrijver, Reflection positivity, rank connectivity, and homomorphism of graphs (MSR Tech Report # MSR-TR-2004-41) ftp://ftp.research.microsoft.com/pub/tr/TR-2004-41.pdf], where they were used to characterize graph homomorphism functions. The goal of this note is to determine the exact rank of these matrices. The result can be rephrased in terms of the dimension of graph algebras, also introduced in the same paper. Yet another version proves that if two k-tuples of nodes behave in the same way from the point of view of graph homomorphisms, then they are equivalent under the automorphism group.

Original languageEnglish
Pages (from-to)962-970
Number of pages9
JournalEuropean Journal of Combinatorics
Volume27
Issue number6
DOIs
Publication statusPublished - Aug 1 2006

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ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics

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