IDEAS home Printed from https://ideas.repec.org/p/tiu/tiutis/16feca8a-db06-46ae-bef6-4d4d338e2c17.html
   My bibliography  Save this paper

A characterization of distance-regular graphs with diameter three

Author

Listed:
  • 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.
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)(This abstract was borrowed from another version of this item.)

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
    as

    Download full text from publisher

    File URL: https://pure.uvt.nl/ws/portalfiles/portal/207001/Characterization.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    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. 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.
    3. van Dam, E.R., 1994. "Regular graphs with four eigenvalues," Research Memorandum FEW 659, 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. van Dam, E.R., 1997. "Three-Class Association Schemes," Research Memorandum 744, Tilburg University, School of Economics and Management.
    2. 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.
    3. Akbari, Saieed & Haemers, Willem H. & Hosseinzadeh, Mohammad Ali & Kabanov, Vladislav V. & Konstantinova, Elena V. & Shalaginov, Leonid, 2021. "Spectra of strongly Deza graphs," Other publications TiSEM 37f09106-0000-4f41-abb6-1, Tilburg University, School of Economics and Management.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    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. & Haemers, W.H., 2002. "Which Graphs are Determined by their Spectrum?," Discussion Paper 2002-66, Tilburg University, Center for Economic Research.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. Jiang, Guisheng & Yu, Guidong & Sun, Wei & Ruan, Zheng, 2018. "The least eigenvalue of graphs whose complements have only two pendent vertices," Applied Mathematics and Computation, Elsevier, vol. 331(C), pages 112-119.
    16. Haemers, W.H., 1996. "Disconnected Vertex Sets and Equidistant Code Pairs," Other publications TiSEM 88f23503-c117-4689-876b-1, Tilburg University, School of Economics and Management.
    17. Haemers, W.H. & Spence, E., 2000. "The Pseudo-Geometric Graphs for Generalised Quadrangles of Order (3,t)," Other publications TiSEM 5ff99d9d-636d-43b2-80ef-c, Tilburg University, School of Economics and Management.
    18. Etienne de Klerk & Monique Laurent, 2020. "Worst-Case Examples for Lasserre’s Measure–Based Hierarchy for Polynomial Optimization on the Hypercube," Mathematics of Operations Research, INFORMS, vol. 45(1), pages 86-98, February.
    19. Haemers, W.H. & Spence, E., 2001. "The pseudo-geometric graphs for generalized quadrangles of order (3,t)," Other publications TiSEM 792e7c74-c02a-4bd4-a2d2-5, Tilburg University, School of Economics and Management.
    20. Gaury, E.G.A., 2000. "Designing pull production control systems : Customization and robustness," Other publications TiSEM c9b49495-f647-4583-b2ef-0, Tilburg University, School of Economics and Management.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:tiu:tiutis:16feca8a-db06-46ae-bef6-4d4d338e2c17. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Richard Broekman (email available below). General contact details of provider: https://www.tilburguniversity.edu/about/schools/economics-and-management/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.