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A Note on the Stability Number of an Orthogonality Graph


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  • Klerk, E. de
  • Pasechnik, D.V.

    (Tilburg University, Center for Economic Research)


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.

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Bibliographic Info

Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 2005-66.

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Date of creation: 2005
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Handle: RePEc:dgr:kubcen:200566

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Keywords: C0; C61;

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Cited by:
  1. Klerk, E. de & Pasechnik, D.V., 2005. "Solving SDP's in Non-commutative Algebras Part I: The Dual-Scaling Algorithm," Discussion Paper 2005-17, Tilburg University, Center for Economic Research.


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