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A characterization of distance-regular graphs with diameter three

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  • Haemers, W.H.

    (Tilburg University, School of Economics and Management)

  • van Dam, E.R.

    (Tilburg University, School of Economics and Management)

Abstract

We characterize the distance-regular graphs with diameter three by giving an expression for the number of vertices at distance two from each given vertex, in terms of the spectrum of the graph.
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Suggested Citation

  • Haemers, W.H. & van Dam, E.R., 1997. "A characterization of distance-regular graphs with diameter three," Other publications TiSEM 16feca8a-db06-46ae-bef6-4, Tilburg University, School of Economics and Management.
    • Handle: RePEc:tiu:tiutis:16feca8a-db06-46ae-bef6-4d4d338e2c17
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    References listed on IDEAS

    as
    1. van Dam, E.R., 1996. "Graphs with few eigenvalues : An interplay between combinatorics and algebra," Other publications TiSEM 93358bfe-49d3-4164-bc75-c, Tilburg University, School of Economics and Management.
    2. van Dam, E.R., 1994. "Regular graphs with four eigenvalues," Research Memorandum FEW 659, Tilburg University, School of Economics and Management.
    3. 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.
    4. Haemers, W.H., 1995. "Interlacing eigenvalues and graphs," Other publications TiSEM 35c08207-2c5c-4387-aaf5-2, Tilburg University, School of Economics and Management.
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    Cited by:

    1. van Dam, E.R. & Fiol, M.A., 2014. "The Laplacian spectral excess theorem for distance-regular graphs," Other publications TiSEM 6188707e-e0eb-4b5f-9b3b-4, 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., 1995. "Bounds on separated pairs of subgraphs, eigenvalues and related polynomials," Other publications TiSEM b667448d-4797-4d27-9929-5, Tilburg University, School of Economics and Management.
    4. van Dam, E.R., 1998. "Bounds on special subsets in graphs, eigenvalues and association schemes," Other publications TiSEM e9bcdd9f-2de0-4750-9ea2-c, Tilburg University, School of Economics and Management.
    5. van Dam, E.R., 1997. "Three-Class Association Schemes," Research Memorandum 744, Tilburg University, School of Economics and Management.
    6. van Dam, E.R., 1995. "Bounds on separated pairs of subgraphs, eigenvalues and related polynomials," Research Memorandum FEW 699, Tilburg University, School of Economics and Management.

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