IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v360y2019icp213-220.html
   My bibliography  Save this article

Total rainbow connection numbers of some special graphs

Author

Listed:
  • Ma, Yingbin
  • Nie, Kairui
  • Jin, Fengxia
  • Wang, Cui

Abstract

In 2008, Chartrand et al. first introduced the concept of rainbow connection. Since then the study of rainbow connection has received considerable attention in the literature, and now it becomes an active topic in graph theory. As a natural generalization, Uchizawa et al. (2013) and Liu et al. (2014) presented the concept of total rainbow connection, respectively. In this paper, we investigate the total rainbow connection numbers of outerplanar graphs with diameter 2. Applying our result, we improve the main result of [X. Huang, X. Li, Y. Shi, J. Yue, Y. Zhao, Rainbow connections for outerplanar graphs with diameter 2 and 3, Applied Mathematics and Computation, 242(2014), 277–280]. Next, we revise the main result of [Y. Liu, Z. Wang, Rainbow Connection Number of the Thorn Graph, Applied Mathematical Sciences, 8(2014), 6373–6377], and determine the total rainbow connection numbers of graphs G, where G are the thorn graph of complete graph Kn*, the thorn graph of the cycle Cn*. At last, we study the rainbow 2-connection numbers of some special graphs.

Suggested Citation

  • Ma, Yingbin & Nie, Kairui & Jin, Fengxia & Wang, Cui, 2019. "Total rainbow connection numbers of some special graphs," Applied Mathematics and Computation, Elsevier, vol. 360(C), pages 213-220.
    • Handle: RePEc:eee:apmaco:v:360:y:2019:i:c:p:213-220
    DOI: 10.1016/j.amc.2019.05.008
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300319303959
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2019.05.008?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. Hui Lei & Shasha Li & Henry Liu & Yongtang Shi, 2018. "Rainbow vertex connection of digraphs," Journal of Combinatorial Optimization, Springer, vol. 35(1), pages 86-107, January.
    2. Hui Jiang & Xueliang Li & Yingying Zhang, 2016. "Upper bounds for the total rainbow connection of graphs," Journal of Combinatorial Optimization, Springer, vol. 32(1), pages 260-266, July.
    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. Ma, Yingbin & Zhang, Xiaoxue, 2023. "Graphs with (strong) proper connection numbers m−3 and m−4," Applied Mathematics and Computation, Elsevier, vol. 445(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. Fiedorowicz, Anna & Sidorowicz, Elżbieta & Sopena, Éric, 2021. "Proper connection and proper-walk connection of digraphs," Applied Mathematics and Computation, Elsevier, vol. 410(C).
    2. Ma, Yingbin & Zhu, Wenhan, 2022. "Some results on the 3‐total‐rainbow index," Applied Mathematics and Computation, Elsevier, vol. 427(C).
    3. Yingbin Ma & Kairui Nie, 2021. "(Strong) Total proper connection of some digraphs," Journal of Combinatorial Optimization, Springer, vol. 42(1), pages 24-39, July.
    4. Guan, Xiaxia & Xue, Lina & Cheng, Eddie & Yang, Weihua, 2019. "Minimum degree and size conditions for the proper connection number of graphs," Applied Mathematics and Computation, Elsevier, vol. 352(C), pages 205-210.
    5. Nie, Kairui & Ma, Yingbin & Sidorowicz, Elżbieta, 2023. "(Strong) Proper vertex connection of some digraphs," Applied Mathematics and Computation, Elsevier, vol. 458(C).
    6. 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.
    7. Gu, Ran & Deng, Bo & Li, Rui, 2019. "Note on directed proper connection number of a random graph," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 169-174.
    8. Ma, Yingbin & Zhang, Xiaoxue, 2023. "Graphs with (strong) proper connection numbers m−3 and m−4," Applied Mathematics and Computation, Elsevier, vol. 445(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:360:y:2019:i:c:p:213-220. 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.