A Note on the Stability Number of an Orthogonality Graph

E. de Klerk, D.V. Pasechnik

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Abstract

We consider the orthogonality graph (n) with 2n vertices corresponding to the vectors {0, 1}n, two vertices adjacent if and only if the Hamming distance between them is n/2.We show that, for n = 16, the stability number of (n) is ( (16)) = 2304, thus proving a conjecture by Galliard [7].The main tool we employ is a recent semidefinite programming relaxation for minimal distance binary codes due to Schrijver [16].Moreover, we give a general condition for Delsarte bound on the (co)cliques in graphs of relations of association schemes to coincide with the ratio bound, and use it to show that for (n) the latter two bounds are equal to 2n/n.
Original languageEnglish
Place of PublicationTilburg
PublisherOperations research
Number of pages11
Volume2005-66
Publication statusPublished - 2005

Publication series

NameCentER Discussion Paper
Volume2005-66

Keywords

  • C0
  • C61

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    de Klerk, E., & Pasechnik, D. V. (2005). A Note on the Stability Number of an Orthogonality Graph. (CentER Discussion Paper; Vol. 2005-66). Operations research.