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Some implications on amorphic association schemes

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  • van Dam, E.R.

    (Tilburg University, School of Economics and Management)

  • Muzychuk, M.

Abstract

We give an overview of results on amorphic association schemes. We give the known constructions of such association schemes, and enumerate most such association schemes on up to 49 vertices. Special attention is paid to cyclotomic association schemes. We give several results on when a strongly regular decomposition of the complete graph is an amorphic association scheme. This includes a new proof of the result that a decomposition of the complete graph into three strongly regular graphs is an amorphic association scheme, and the new result that a strongly regular decomposition of the complete graph for which the union of any two relations is again strongly regular must be an amorphic association scheme.
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Suggested Citation

  • van Dam, E.R. & Muzychuk, M., 2010. "Some implications on amorphic association schemes," Other publications TiSEM 4eb753bb-9046-44ea-b3d0-e, Tilburg University, School of Economics and Management.
    • Handle: RePEc:tiu:tiutis:4eb753bb-9046-44ea-b3d0-e23b777f69cc
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    References listed on IDEAS

    as
    1. van Dam, E.R., 2001. "Strongly Regular Decompositions of the Complete Graph," Discussion Paper 2001-61, Tilburg University, Center for Economic Research.
    2. Bussemaker, F.C. & Haemers, W.H. & Spence, E., 2000. "The search for pseudo orthogonal Latin squares of order six," Other publications TiSEM 860514f0-4ac6-4563-bf5c-b, Tilburg University, School of Economics and Management.
    3. van Dam, E.R., 1997. "Three-Class Association Schemes," Research Memorandum 744, Tilburg University, School of Economics and Management.
    4. van Dam, E.R. & de Caen, D., 1999. "Fissions of classical self-dual association schemes," Other publications TiSEM cbb05a3b-6be6-4f3a-8ac9-2, Tilburg University, School of Economics and Management.
    5. van Dam, E.R., 2000. "A characterization of association schemes from affine spaces," Other publications TiSEM 930fccbb-dd49-4a6f-b595-2, Tilburg University, School of Economics and Management.
    Full references (including those not matched with items on IDEAS)

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    JEL classification:

    • C0 - Mathematical and Quantitative Methods - - General

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