IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v325y2018icp309-321.html
   My bibliography  Save this article

Cospectrality of graphs with respect to distance matrices

Author

Listed:
  • Aouchiche, Mustapha
  • Hansen, Pierre

Abstract

The distance, distance Laplacian and distance signless Laplacian spectra of a connected graph G are the spectra of the distance, distance Laplacian and distance signless Laplacian matrices of G. Two graphs are said to be cospectral with respect to the distance (resp. distance Laplacian or distance signless Laplacian) matrix if they share the same distance (resp. distance Laplacian or distance signless Laplacian) spectrum. If a graph G does not share its spectrum with any other graph, we say G is determined by its spectrum. In this paper we are interested in the cospectrality with respect to the three distance matrices. First, we report on a numerical study in which we looked into the spectra of the distance, distance Laplacian and distance signless Laplacian matrices of all the connected graphs on up to 10 vertices. Then, we prove some theoretical results about what we can deduce about a graph from these spectra. Among other results we identify some of the graphs determined by their distance Laplacian or distance signless Laplacian spectra.

Suggested Citation

  • Aouchiche, Mustapha & Hansen, Pierre, 2018. "Cospectrality of graphs with respect to distance matrices," Applied Mathematics and Computation, Elsevier, vol. 325(C), pages 309-321.
    • Handle: RePEc:eee:apmaco:v:325:y:2018:i:c:p:309-321
    DOI: 10.1016/j.amc.2017.12.025
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300317308846
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2017.12.025?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. van Dam, E.R. & Haemers, W.H. & Koolen, J.H., 2006. "Cospectral Graphs and the Generalized Adjacency Matrix," Discussion Paper 2006-31, 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.
    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. Rakshith, B.R. & Das, Kinkar Chandra, 2023. "On distance Laplacian spectral determination of complete multipartite graphs," Applied Mathematics and Computation, Elsevier, vol. 443(C).
    2. Abdollah Alhevaz & Maryam Baghipur & Hilal A. Ganie & Yilun Shang, 2019. "On the Generalized Distance Energy of Graphs," Mathematics, MDPI, vol. 8(1), pages 1-16, December.
    3. Abiad, Aida & Alfaro, Carlos A., 2021. "Enumeration of cospectral and coinvariant graphs," Applied Mathematics and Computation, Elsevier, vol. 408(C).

    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. & 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., 2007. "Developments on Spectral Characterizations of Graphs," Other publications TiSEM 3827c785-7b51-4bcd-aea3-f, Tilburg University, School of Economics and Management.
    3. Saeree Wananiyakul & Jörn Steuding & Janyarak Tongsomporn, 2022. "How to Distinguish Cospectral Graphs," Mathematics, MDPI, vol. 10(24), pages 1-24, December.
    4. Tianyi Bu & Lizhu Sun & Wenzhe Wang & Jiang Zhou, 2014. "Main Q-eigenvalues and generalized Q-cospectrality of graphs," Indian Journal of Pure and Applied Mathematics, Springer, vol. 45(4), pages 531-538, August.
    5. Xiaoyun Yang & Ligong Wang, 2020. "Laplacian Spectral Characterization of (Broken) Dandelion Graphs," Indian Journal of Pure and Applied Mathematics, Springer, vol. 51(3), pages 915-933, September.
    6. Haemers, W.H., 2005. "Matrices and Graphs," Other publications TiSEM 94b6bd28-71e7-41d3-b978-c, Tilburg University, School of Economics and Management.
    7. 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.
    8. B. R. Rakshith, 2022. "Signless Laplacian spectral characterization of some disjoint union of graphs," Indian Journal of Pure and Applied Mathematics, Springer, vol. 53(1), pages 233-245, March.
    9. van Dam, E.R. & Haemers, W.H. & Koolen, J.H., 2006. "Cospectral Graphs and the Generalized Adjacency Matrix," Discussion Paper 2006-31, Tilburg University, Center for Economic Research.
    10. Haemers, W.H. & Ramezani, F., 2009. "Graphs Cospectral with Kneser Graphs," Discussion Paper 2009-76, Tilburg University, Center for Economic Research.
    11. Estrada, Ernesto, 2007. "Graphs (networks) with golden spectral ratio," Chaos, Solitons & Fractals, Elsevier, vol. 33(4), pages 1168-1182.
    12. van Dam, E.R. & Haemers, W.H., 2010. "An Odd Characterization of the Generalized Odd Graphs," Other publications TiSEM 2478f418-ae83-4ac3-8742-2, Tilburg University, School of Economics and Management.
    13. Abiad, A. & Haemers, W.H., 2012. "Cospectral Graphs and Regular Orthogonal Matrices of Level 2," Other publications TiSEM c656ae2c-dc83-44be-906c-b, Tilburg University, School of Economics and Management.
    14. 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.
    15. Abiad, A. & Haemers, W.H., 2012. "Cospectral Graphs and Regular Orthogonal Matrices of Level 2," Discussion Paper 2012-042, Tilburg University, Center for Economic Research.
    16. Al-Yakoob, Salem & Kanso, Ali & Stevanović, Dragan, 2022. "On Hosoya’s dormants and sprouts," Applied Mathematics and Computation, Elsevier, vol. 430(C).
    17. Mao, Ding & Wang, Peng & Fang, Yi-Ping & Ni, Long, 2024. "Securing heat-supply against seismic risks: A two-staged framework for assessing vulnerability and economic impacts in district heating networks," Applied Energy, Elsevier, vol. 369(C).
    18. Wang, Xiangrong & Trajanovski, Stojan & Kooij, Robert E. & Van Mieghem, Piet, 2016. "Degree distribution and assortativity in line graphs of complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 445(C), pages 343-356.
    19. 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.
    20. Yuan, Bo-Jun & Wang, Yi & Xu, Jing, 2020. "Characterizing the mixed graphs with exactly one positive eigenvalue and its application to mixed graphs determined by their H-spectra," Applied Mathematics and Computation, Elsevier, vol. 380(C).

    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:eee:apmaco:v:325:y:2018:i:c:p:309-321. 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: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.