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Spectral characterizations of some distance-regular graphs

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  • van Dam, E.R.

    (Tilburg University, School of Economics and Management)

  • Haemers, W.H.

    (Tilburg University, School of Economics and Management)

Abstract

When can one see from the spectrum of a graph whether it is distance-regular or not?We give some new results for when this is the case.As a consequence we find (among others) that the following distance-regular graphs are uniquely determined by their spectrum: The collinearity graphs of the generalized octagons of order (2; 1), (3; 1) and (4; 1), the Biggs-Smith graph, the M22 graph, and the coset graphs of the doubly truncated binary Golay code and the extended ternary Golay code.
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Suggested Citation

  • van Dam, E.R. & Haemers, W.H., 2002. "Spectral characterizations of some distance-regular graphs," Other publications TiSEM 416915a8-90ef-4af9-ae5d-d, Tilburg University, School of Economics and Management.
    • Handle: RePEc:tiu:tiutis:416915a8-90ef-4af9-ae5d-ddc66e83ce1b
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    1. 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.
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    1. 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.
    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., 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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    1. van Dam, E.R. & Haemers, W.H., 2000. "Spectral Characterizations of Some Distance-Regular Graphs," Other publications TiSEM 21d88deb-8836-4902-87a7-c, Tilburg University, School of Economics and Management.
    2. 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.
    3. 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.
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    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.
    6. van Dam, E.R., 1997. "Three-Class Association Schemes," Research Memorandum 744, Tilburg University, School of Economics and Management.
    7. 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.
    8. 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.
    9. Peeters, M.J.P., 1997. "Strongly regular graphs that are locally a disjoint union of hexagons," Other publications TiSEM 2691bb15-9a34-40cc-95ff-2, Tilburg University, School of Economics and Management.

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