IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v458y2023ics0096300323003946.html
   My bibliography  Save this article

Note for the conjecture on the generalized 4-connectivity of total graphs of the complete bipartite graph

Author

Listed:
  • Li, Yinkui
  • Wei, Liqun

Abstract

The generalized k-connectivity κk(G) of a graph G, introduced by Hager in 1985, is a natural generalization of the concept of connectivity κ(G), which is just for k=2. Rongxia Hao et al. determined the generalized 4-connectivity of the total graphs of the complete equipartition bipartite graph and conjectured that κ4(T(Km,m+1))=2m−1 and κ4(T(Km,n))=2m for n>m+1 and m≥4 in [Appl. Math. Comput. 422 (2022)]. In this paper, we solved this conjecture.

Suggested Citation

  • Li, Yinkui & Wei, Liqun, 2023. "Note for the conjecture on the generalized 4-connectivity of total graphs of the complete bipartite graph," Applied Mathematics and Computation, Elsevier, vol. 458(C).
    • Handle: RePEc:eee:apmaco:v:458:y:2023:i:c:s0096300323003946
    DOI: 10.1016/j.amc.2023.128225
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300323003946
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2023.128225?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. Zhao, Shu-Li & Hao, Rong-Xia & Wei, Chao, 2022. "Internally disjoint trees in the line graph and total graph of the complete bipartite graph," Applied Mathematics and Computation, Elsevier, vol. 422(C).
    2. Li, Shasha & Tu, Jianhua & Yu, Chenyan, 2016. "The generalized 3-connectivity of star graphs and bubble-sort graphs," Applied Mathematics and Computation, Elsevier, vol. 274(C), pages 41-46.
    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. Hong Chang & Xueliang Li & Colton Magnant & Zhongmei Qin, 2018. "The $$(k,\ell )$$ ( k , ℓ ) -proper index of graphs," Journal of Combinatorial Optimization, Springer, vol. 36(2), pages 458-471, August.
    2. Catanzaro, Daniele & Frohn, Martin & Gascuel, Olivier & Pesenti, Raffaele, 2023. "A Massively Parallel Exact Solution Algorithm for the Balanced Minimum Evolution Problem," LIDAM Discussion Papers CORE 2023001, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. Catanzaro, Daniele & Frohn, Martin & Gascuel, Olivier & Pesenti, Raffaele, 2021. "A Tutorial on the Balanced Minimum Evolution Problem," LIDAM Discussion Papers CORE 20210, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. Li, Shasha & Zhao, Yan & Li, Fengwei & Gu, Ruijuan, 2019. "The generalized 3-connectivity of the Mycielskian of a graph," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 882-890.
    5. Zhang, Guozhen & Wang, Dajin, 2019. "Structure connectivity and substructure connectivity of bubble-sort star graph networks," Applied Mathematics and Computation, Elsevier, vol. 363(C), pages 1-1.
    6. Zhao, Shu-Li & Hao, Rong-Xia & Wei, Chao, 2022. "Internally disjoint trees in the line graph and total graph of the complete bipartite graph," Applied Mathematics and Computation, Elsevier, vol. 422(C).
    7. Li, Hengzhe & Ma, Yingbin & Yang, Weihua & Wang, Yifei, 2017. "The generalized 3-connectivity of graph products," Applied Mathematics and Computation, Elsevier, vol. 295(C), pages 77-83.
    8. Gao, Hui & Lv, Benjian & Wang, Kaishun, 2018. "Two lower bounds for generalized 3-connectivity of Cartesian product graphs," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 305-313.
    9. Catanzaro, Daniele & Frohn, Martin & Pesenti, Raffaele, 2021. "A Massively Parallel Exact Solution Algorithm for the Balanced Minimum Evolution Problem," LIDAM Discussion Papers CORE 2021023, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    10. Catanzaro, Daniele & Frohn, Martin & Gascuel, Olivier & Pesenti, Raffaele, 2022. "A tutorial on the balanced minimum evolution problem," European Journal of Operational Research, Elsevier, vol. 300(1), pages 1-19.
    11. Li, Hengzhe & Wang, Jiajia, 2018. "The λ3-connectivity and κ3-connectivity of recursive circulants," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 750-757.
    12. Zhao, Shu-Li & Hao, Rong-Xia, 2019. "The generalized 4-connectivity of exchanged hypercubes," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 342-353.
    13. Mao, Yaping, 2017. "Constructing edge-disjoint Steiner paths in lexicographic product networks," Applied Mathematics and Computation, Elsevier, vol. 308(C), pages 1-10.
    14. Catanzaro, Daniele & Frohn, Martin & Pesenti, Raffaele, 2021. "On Numerical Stability and Statistical Consistency of the Balanced Minimum Evolution Problem," LIDAM Discussion Papers CORE 2021026, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).

    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:458:y:2023:i:c:s0096300323003946. 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.