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Three-Class Association Schemes

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  • van Dam, E.R.

    (Tilburg University, Faculty of Economics)

Abstract

We study (symmetric) three-class association schemes.The graphs with four distinct eigenvalues which are one of the relations of such a scheme are characterized.We give an overview of most known constructions, and obtain necessary conditions for existence.A list of feasible parameter sets on at most 100 vertices is generated.
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Suggested Citation

  • van Dam, E.R., 1997. "Three-Class Association Schemes," Research Memorandum 744, Tilburg University, School of Economics and Management.
    • Handle: RePEc:tiu:tiurem:11390cd9-c602-4a0c-9f25-b431091b4516
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    References listed on IDEAS

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    1. van Dam, E.R. & Haemers, W.H., 1995. "A characterization of distance-regular graphs with diameter three," Research Memorandum FEW 695, Tilburg University, School of Economics and Management.
    2. Coster, M.J., 1994. "Quadratic forms in design theory," Research Memorandum FEW 635, Tilburg University, School of Economics and Management.
    3. van Dam, E.R. & Spence, E., 1996. "Small Regular Graphs with Four Eigenvalues," Research Memorandum 723, Tilburg University, School of Economics and Management.
    4. van Dam, E.R., 1994. "Regular graphs with four eigenvalues," Research Memorandum FEW 659, Tilburg University, School of Economics and Management.
    5. Haemers, W.H., 1996. "Distance-regularity and the spectrum of graphs," Other publications TiSEM 0b0a4a2f-4eec-4ab3-b718-3, Tilburg University, School of Economics and Management.
    6. Coster, M.J., 1994. "Quadratic forms in design theory," Other publications TiSEM 1bba10fd-8af3-4dbe-9f69-0, Tilburg University, School of Economics and Management.
    7. Haemers, W.H. & Coster, M.J., 1995. "Quasi-symmetric designs related to the triangular graph," Other publications TiSEM cbc5cd93-f57a-442b-84b2-7, Tilburg University, School of Economics and Management.
    8. Haemers, W.H., 1995. "Interlacing eigenvalues and graphs," Other publications TiSEM 35c08207-2c5c-4387-aaf5-2, Tilburg University, School of Economics and Management.
    9. Haemers, W.H. & Touchev, V.D., 1996. "Spreads in strongly regular graphs," Other publications TiSEM baf73ad8-e852-4528-b0b5-c, Tilburg University, School of Economics and Management.
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    Citations

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    Cited by:

    1. van Dam, E.R. & Martin, W.J. & Muzychuk, M., 2010. "Uniformity in Association schemes and Coherent Configurations : Cometric Q-Antipodal Schemes and Linked Systems," Other publications TiSEM 3f994561-285b-4be1-88e5-7, Tilburg University, School of Economics and Management.
    2. van Dam, E.R. & Martin, W.J. & Muzychuk, M., 2010. "Uniformity in Association schemes and Coherent Configurations : Cometric Q-Antipodal Schemes and Linked Systems," Discussion Paper 2010-10, Tilburg University, Center for Economic Research.
    3. van Dam, E.R. & Haemers, W.H. & Koolen, J.H. & Spence, E., 2005. "Characterizing Distance-Regularity of Graphs by the Spectrum," Discussion Paper 2005-19, Tilburg University, Center for Economic Research.
    4. Bussemaker, F.C. & Haemers, W.H. & Spence, E., 1999. "The Search for Pseudo Orthogonal Latin Squares of Order Six," Other publications TiSEM eaa43e8f-0be1-4b54-a567-f, Tilburg University, School of Economics and Management.
    5. 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.
    6. Bussemaker, F.C. & Haemers, W.H. & Spence, E., 1999. "The Search for Pseudo Orthogonal Latin Squares of Order Six," Research Memorandum 780, Tilburg University, School of Economics and Management.
    7. Fiala, N.C. & Haemers, W.H., 2003. "5-Chromatic Strongly Regular Graphs," Other publications TiSEM 16d4bde1-141a-428d-9633-b, Tilburg University, School of Economics and Management.
    8. 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.
    9. van Dam, E.R. & Muzychuk, M., 2008. "Some Implications on Amorphic Association Schemes," Other publications TiSEM 2b039ac4-0edb-4536-801a-c, Tilburg University, School of Economics and Management.
    10. Fiala, N.C. & Haemers, W.H., 2003. "5-Chromatic Strongly Regular Graphs," Discussion Paper 2003-45, Tilburg University, Center for Economic Research.
    11. van Dam, E.R. & Muzychuk, M., 2008. "Some Implications on Amorphic Association Schemes," Discussion Paper 2008-56, Tilburg University, Center for Economic Research.

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