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An Odd Characterization of the Generalized Odd Graphs

Author

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  • van Dam, E.R.

    (Tilburg University, Center For Economic Research)

  • Haemers, W.H.

    (Tilburg University, Center For Economic Research)

Abstract

We show that any connected regular graph with d + 1 distinct eigenvalues and odd-girth 2d + 1 is distance-regular, and in particular that it is a generalized odd graph.
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Suggested Citation

  • van Dam, E.R. & Haemers, W.H., 2010. "An Odd Characterization of the Generalized Odd Graphs," Discussion Paper 2010-47, Tilburg University, Center for Economic Research.
    • Handle: RePEc:tiu:tiucen:2478f418-ae83-4ac3-8742-227315874e96
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    File URL: https://pure.uvt.nl/ws/portalfiles/portal/1220674/2010-47.pdf
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    References listed on IDEAS

    as
    1. van Dam, E.R. & Haemers, W.H., 2007. "Developments on Spectral Characterizations of Graphs," Discussion Paper 2007-33, Tilburg University, Center for Economic Research.
    2. 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.
    3. van Dam, E.R. & Haemers, W.H., 1998. "Graphs with constant mu and mu-bar," Other publications TiSEM 3cba5bf4-ad2f-465d-a9a2-a, Tilburg University, School of Economics and Management.
    4. van Dam, E.R., 2008. "The spectral excess theorem for distance-regular graphs : A global (over)view," Other publications TiSEM 35daf99b-ad28-4e21-8b1f-6, Tilburg University, School of Economics and Management.
    5. 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.
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    Citations

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    Cited by:

    1. van Dam, E.R. & Fiol, M.A., 2012. "A short proof of the odd-girth theorem," Other publications TiSEM ad0d371c-9934-4a42-83ef-2, Tilburg University, School of Economics and Management.

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    More about this item

    Keywords

    distance-regular graphs; generalized odd graphs; odd-girth; spectra of graphs; spectral excess theorem; spectral characterization;
    All these keywords.

    JEL classification:

    • C0 - Mathematical and Quantitative Methods - - General

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