IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v339y2018icp750-757.html
   My bibliography  Save this article

The λ3-connectivity and κ3-connectivity of recursive circulants

Author

Listed:
  • Li, Hengzhe
  • Wang, Jiajia

Abstract

Let S be a set of at least two vertices in a graph G. A subtree T of G is a S-Steiner tree if S ⊆ V (T). Two S-Steiner trees T1 and T2 are edge-disjoint (resp. internally disjoint) if E(T1)∩E(T2)=∅ (resp. E(T1)∩E(T2)=∅ and V(T1)∩V(T2)=S). Let λG(S) (resp. κG(S)) be the maximum number of edge-disjoint (resp. internally disjoint) S-Steiner trees in G, and let λk(G) (κk(G)) be the minimum λG(S) (resp. κG(S)) for S ranges over all k-subsets of V(G). Clearly, λ2(G) (resp. κ2(G)) is the classical edge-connectivity λ(G) (resp. connectivity κ(G)). In this paper, we study the λ3-connectivity and κ3-connectivity of a recursive circulant G, determine λ3(G)=δ(G)−1 for each recursive circulant G, and κ3(G)=δ(G)−1 for each recursive circulant G except G≅G(2m, 2).

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:339:y:2018:i:c:p:750-757
    DOI: 10.1016/j.amc.2018.07.065
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300318306313
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2018.07.065?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. Yuefang Sun & Xueliang Li, 2017. "On the difference of two generalized connectivities of a graph," Journal of Combinatorial Optimization, Springer, vol. 33(1), pages 283-291, January.
    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.
    3. Shasha Li & Xueliang Li, 2012. "Note on the hardness of generalized connectivity," Journal of Combinatorial Optimization, Springer, vol. 24(3), pages 389-396, October.
    4. 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.
    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. 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.
    2. 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).
    3. 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.
    4. 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.
    5. 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.
    6. 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).
    7. 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.
    8. 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).
    9. 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).
    10. Yuefang Sun & Chenchen Wu & Xiaoyan Zhang & Zhao Zhang, 2022. "Computation and algorithm for the minimum k-edge-connectivity of graphs," Journal of Combinatorial Optimization, Springer, vol. 44(3), pages 1741-1752, October.
    11. Zhu, Wen-Han & Hao, Rong-Xia & Feng, Yan-Quan & Lee, Jaeun, 2023. "The 3-path-connectivity of the k-ary n-cube," Applied Mathematics and Computation, Elsevier, vol. 436(C).
    12. 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.
    13. Lily Chen & Xueliang Li & Mengmeng Liu & Yaping Mao, 2017. "A solution to a conjecture on the generalized connectivity of graphs," Journal of Combinatorial Optimization, Springer, vol. 33(1), pages 275-282, January.
    14. Hongyu Liang & Tiancheng Lou & Haisheng Tan & Yuexuan Wang & Dongxiao Yu, 2015. "On the complexity of connectivity in cognitive radio networks through spectrum assignment," Journal of Combinatorial Optimization, Springer, vol. 29(2), pages 472-487, February.
    15. 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).
    16. Yuefang Sun & Chenchen Wu & Xiaoyan Zhang & Zhao Zhang, 0. "Computation and algorithm for the minimum k-edge-connectivity of graphs," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-12.
    17. 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.
    18. Shasha Li & Wei Li & Yongtang Shi & Haina Sun, 2017. "On minimally 2-connected graphs with generalized connectivity $$\kappa _{3}=2$$ κ 3 = 2," Journal of Combinatorial Optimization, Springer, vol. 34(1), pages 141-164, July.
    19. 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.
    20. Quach, Sara & Jebarajakirthy, Charles & Thaichon, Park, 2017. "Aesthetic labor and visible diversity: The role in retailing service encounters," Journal of Retailing and Consumer Services, Elsevier, vol. 38(C), pages 34-43.

    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:339:y:2018:i:c:p:750-757. 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.