IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v430y2022ics0096300322003071.html
   My bibliography  Save this article

On Hosoya’s dormants and sprouts

Author

Listed:
  • Al-Yakoob, Salem
  • Kanso, Ali
  • Stevanović, Dragan

Abstract

The study of cospectral graphs is one of the traditional topics of spectral graph theory. Initial expectation by theoretical chemists Günthard and Primas in 1956 that molecular graphs are characterized by the multiset of eigenvalues of the adjacency matrix was quickly refuted by the existence of numerous examples of cospectral graphs in both chemical and mathematical literature. This work was further motivated by Fisher in 1966 in the influential study that investigated whether one can “hear” the shape of a (discrete) drum, which has led over the years to the construction of many cospectral graphs. These findings culminated in setting the ground for the Godsil-McKay local switching and the Schwenk’s use of coalescences, both of which were used to show (around the 1980s) that almost all trees have cospectral mates. Recently, enumerations of cospectral graphs with up to 12 vertices by Haemers and Spence and by Brouwer and Spence have led to the conjecture that, on the contrary, “almost all graphs are likely to be determined by their spectrum”. This conjecture paved the way for myriad of results showing that various special types of graphs are determined by their spectra.

Suggested Citation

  • Al-Yakoob, Salem & Kanso, Ali & Stevanović, Dragan, 2022. "On Hosoya’s dormants and sprouts," Applied Mathematics and Computation, Elsevier, vol. 430(C).
    • Handle: RePEc:eee:apmaco:v:430:y:2022:i:c:s0096300322003071
    DOI: 10.1016/j.amc.2022.127233
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300322003071
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2022.127233?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., 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.
    Full references (including those not matched with items on IDEAS)

    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. 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.
    2. 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.
    3. Haemers, W.H. & Ramezani, F., 2009. "Graphs Cospectral with Kneser Graphs," Discussion Paper 2009-76, Tilburg University, Center for Economic Research.
    4. 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.
    5. 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.
    6. 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.
    7. Xue, Jie & Liu, Shuting & Shu, Jinlong, 2018. "The complements of path and cycle are determined by their distance (signless) Laplacian spectra," Applied Mathematics and Computation, Elsevier, vol. 328(C), pages 137-143.
    8. 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).
    9. Lei, Xingyu & Wang, Jianfeng, 2022. "Spectral determination of graphs with one positive anti-adjacency eigenvalue," Applied Mathematics and Computation, Elsevier, vol. 422(C).
    10. Fei Wen & Qiongxiang Huang & Xueyi Huang & Fenjin Liu, 2015. "The spectral characterization of wind-wheel graphs," Indian Journal of Pure and Applied Mathematics, Springer, vol. 46(5), pages 613-631, October.
    11. Maiorino, Enrico & Rizzi, Antonello & Sadeghian, Alireza & Giuliani, Alessandro, 2017. "Spectral reconstruction of protein contact networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 471(C), pages 804-817.
    12. Saeree Wananiyakul & Jörn Steuding & Janyarak Tongsomporn, 2022. "How to Distinguish Cospectral Graphs," Mathematics, MDPI, vol. 10(24), pages 1-24, December.
    13. Fei Wen & Qiongxiang Huang & Xueyi Huang & Fenjin Liu, 2018. "On the Laplacian spectral characterization of Π-shape trees," Indian Journal of Pure and Applied Mathematics, Springer, vol. 49(3), pages 397-411, September.
    14. Haemers, W.H. & Ramezani, F., 2009. "Graphs Cospectral with Kneser Graphs," Other publications TiSEM 386fd2ad-65f2-42b6-9dfc-1, Tilburg University, School of Economics and Management.
    15. Xihe Li & Ligong Wang & Shangyuan Zhang, 2018. "The Signless Laplacian Spectral Radius of Some Strongly Connected Digraphs," Indian Journal of Pure and Applied Mathematics, Springer, vol. 49(1), pages 113-127, March.
    16. 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.
    17. Lizhu Sun & Wenzhe Wang & Jiang Zhou & Changjiang Bu, 2015. "Laplacian spectral characterization of some graph join," Indian Journal of Pure and Applied Mathematics, Springer, vol. 46(3), pages 279-286, June.
    18. Haemers, W.H., 2005. "Matrices and Graphs," Other publications TiSEM 94b6bd28-71e7-41d3-b978-c, Tilburg University, School of Economics and Management.
    19. 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.
    20. 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.

    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:430:y:2022:i:c:s0096300322003071. 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.