A Note on the Stability Number of an Orthogonality Graph

CentER Discussion Paper No. 2005-66

10 Pages Posted: 18 May 2005

See all articles by Etienne de Klerk

Etienne de Klerk

Tilburg University

Dmitrii V. Pasechnik

Tilburg University - Center for Economic Research (CentER)

Date Written: May 2005

Abstract

We consider the orthoganality graph omega(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 omega(n) is alpha(omega(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 omega(n) the latter two bounds are equal 2n/n.

Keywords: Semidefinite programming, minimal distance codes, stability number, orthoganality graph, Hamming association scheme, Delsarte bound

JEL Classification: C0, C61

Suggested Citation

de Klerk, Etienne and Pasechnik, Dmitrii V., A Note on the Stability Number of an Orthogonality Graph (May 2005). CentER Discussion Paper No. 2005-66. Available at SSRN: https://ssrn.com/abstract=722477 or http://dx.doi.org/10.2139/ssrn.722477

Etienne De Klerk

Tilburg University ( email )

P.O. Box 90153
Tilburg, 5000 LE
Netherlands

Dmitrii V. Pasechnik (Contact Author)

Tilburg University - Center for Economic Research (CentER) ( email )

P.O. Box 90153
Tilburg, 5000 LE
Netherlands

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