Three class association schemes

Home Welcome Authors 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. If you download any of these files, we would appreciate to receive an e-mail which lets us know that you have done so.