Three class association schemes




Kris Coolsaet

Jan Degraer

Below we list the association schemes described in the paper

Degraer J., Coolsaet K., Classification of three-class association schemes using backtracking with dynamic variable ordering, Discrete Mathematics, Vol 300, No. 1-3, pp. 71-81, 2005.
Each file (a UNIX text file compressed with gzip) contains the list of association schemes for a given parameter set. Association schemes in the file are represented by square symmetric matrices with entries i at position p,q if and only if points numbered p and q are in relation Ri.

  • On 35 points. These 35 schemes arise from 22 different strongly regular graphs. Six of them arise from solutions of the Kirkmans schoolgirl problem.
  • On 40 points. These 3 schemes arise from 2 different strongly regular graphs.
  • On 45 points. There are 764 schemes in this list.
  • On 64 points. There are 94 schemes in this list. Relation 1 of this scheme determines a distance regular antipodal cover of the complete graph K16.

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Last update: July 1, 2005