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Small Regular Graphs with Four Eigenvalues

Author

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  • van Dam, E.R.

    (Tilburg University, Faculty of Economics)

  • Spence, E.

Abstract

For most feasible spectra of connected regular graphs with four distinct eigenvalues and at most 30 vertices we find all such graphs, using both theoretic and computer results.
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Suggested Citation

  • van Dam, E.R. & Spence, E., 1996. "Small Regular Graphs with Four Eigenvalues," Research Memorandum 723, Tilburg University, School of Economics and Management.
    • Handle: RePEc:tiu:tiurem:b0236991-9ca8-436e-b88b-399d940deab2
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    File URL: https://pure.uvt.nl/ws/portalfiles/portal/523973/723.pdf
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    References listed on IDEAS

    as
    1. van Dam, E.R., 1994. "Regular graphs with four eigenvalues," Research Memorandum FEW 659, Tilburg University, School of Economics and Management.
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    Citations

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    Cited by:

    1. Haemers, W.H. & Omidi, G.R., 2010. "Universal Adjacency Matrices with Two Eigenvalues," Other publications TiSEM 932a73a8-9fae-44ec-9ce5-7, Tilburg University, School of Economics and Management.
    2. van Dam, E.R. & Spence, E., 2003. "Combinatorial Designs with Two Singular Values II. Partial Geometric Designs," Other publications TiSEM fec47f57-9bec-453d-8275-8, Tilburg University, School of Economics and Management.
    3. van Dam, E.R. & Omidi, G.R., 2013. "Strongly walk-regular grapsh," Other publications TiSEM fbc6dff1-78cc-4d7c-a6c8-e, Tilburg University, School of Economics and Management.
    4. Haemers, W.H. & Kharaghani, H. & Meulenberg, M.A., 2010. "Divisible Design Graphs," Discussion Paper 2010-19, Tilburg University, Center for Economic Research.
    5. van Dam, E.R. & Spence, E., 2005. "Combinatorial designs with two singular values II. Partial geometric designs," Other publications TiSEM e23b8b46-4f9e-4d76-b792-d, Tilburg University, School of Economics and Management.
    6. van Dam, E.R. & Haemers, W.H., 2003. "Which graphs are determined by their spectrum?," Other publications TiSEM a9a1857e-13ce-4da7-bcca-b, Tilburg University, School of Economics and Management.
    7. van Dam, E.R. & Spence, E., 2003. "Combinatorial Designs with Two Singular Values I. Uniform Multiplicative Designs," Discussion Paper 2003-67, Tilburg University, Center for Economic Research.
    8. van Dam, E.R. & Omidi, G.R., 2011. "Graphs whose normalized laplacian has three eigenvalues," Other publications TiSEM d3b7fa76-22b5-4a9a-8706-a, Tilburg University, School of Economics and Management.
    9. Haemers, W.H. & Omidi, G.R., 2010. "Universal Adjacency Matrices with Two Eigenvalues," Discussion Paper 2010-119, Tilburg University, Center for Economic Research.
    10. van Dam, E.R. & de Caen, D. & Spence, E., 1999. "A nonregular analogue of conference graphs," Other publications TiSEM 2354d510-0aeb-4504-917d-5, Tilburg University, School of Economics and Management.
    11. van Dam, E.R., 1997. "Three-Class Association Schemes," Research Memorandum 744, Tilburg University, School of Economics and Management.
    12. van Dam, E.R. & Spence, E., 2003. "Combinatorial Designs with Two Singular Values II. Partial Geometric Designs," Discussion Paper 2003-94, Tilburg University, Center for Economic Research.
    13. Estrada, Ernesto, 2007. "Graphs (networks) with golden spectral ratio," Chaos, Solitons & Fractals, Elsevier, vol. 33(4), pages 1168-1182.
    14. van Dam, E.R. & Spence, E., 2003. "Combinatorial Designs with Two Singular Values I. Uniform Multiplicative Designs," Other publications TiSEM 87fabd1b-6be0-4f99-b7a8-5, Tilburg University, School of Economics and Management.
    15. Haemers, W.H. & Kharaghani, H. & Meulenberg, M.A., 2010. "Divisible Design Graphs," Other publications TiSEM f3ab9fe7-be24-43f3-8eff-9, Tilburg University, School of Economics and Management.
    16. van Dam, E.R. & Haemers, W.H., 2002. "Which Graphs are Determined by their Spectrum?," Discussion Paper 2002-66, Tilburg University, Center for Economic Research.
    17. van Dam, E.R. & Haemers, W.H., 2002. "Which Graphs are Determined by their Spectrum?," Other publications TiSEM f163dbe4-3669-4a99-bc19-7, Tilburg University, School of Economics and Management.

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    2. Estrada, Ernesto, 2007. "Graphs (networks) with golden spectral ratio," Chaos, Solitons & Fractals, Elsevier, vol. 33(4), pages 1168-1182.
    3. 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.
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    10. van Dam, E.R. & Spence, E., 2003. "Combinatorial Designs with Two Singular Values II. Partial Geometric Designs," Discussion Paper 2003-94, Tilburg University, Center for Economic Research.
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    12. 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.
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    15. Haemers, W.H. & Kharaghani, H. & Meulenberg, M.A., 2010. "Divisible Design Graphs," Discussion Paper 2010-19, Tilburg University, Center for Economic Research.
    16. van Dam, E.R. & Omidi, G.R., 2011. "Graphs whose normalized laplacian has three eigenvalues," Other publications TiSEM d3b7fa76-22b5-4a9a-8706-a, Tilburg University, School of Economics and Management.
    17. Peeters, M.J.P., 1994. "On the p-ranks of the adjacency matrices of distance-regular graphs," Research Memorandum FEW 656, Tilburg University, School of Economics and Management.
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    Keywords

    eigenvalues; graphs;

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