IDEAS home Printed from https://ideas.repec.org/a/spr/jcomop/v42y2021i1d10.1007_s10878-021-00738-w.html
   My bibliography  Save this article

(Strong) Total proper connection of some digraphs

Author

Listed:
  • Yingbin Ma

    (Henan Normal University)

  • Kairui Nie

    (Henan Normal University)

Abstract

The total proper connection number of a given digraph D, represented by $$\overrightarrow{tpc}(D)$$ tpc → ( D ) , denotes the smallest number of colors needed for making D total proper connected. The strong total proper connection number of D, represented by $$\overrightarrow{stpc}(D)$$ stpc → ( D ) , shows the smallest number of colors required for making D strong total proper connected. In the present work, we represent some preliminary findings on $$\overrightarrow{tpc}(D)$$ tpc → ( D ) and $$\overrightarrow{stpc}(D)$$ stpc → ( D ) . Moreover, findings on the (strong) total proper connection numbers of biorientations of graphs, circle digraphs, circulant digraphs and cacti digraphs are provided.

Suggested Citation

  • Yingbin Ma & Kairui Nie, 2021. "(Strong) Total proper connection of some digraphs," Journal of Combinatorial Optimization, Springer, vol. 42(1), pages 24-39, July.
  • Handle: RePEc:spr:jcomop:v:42:y:2021:i:1:d:10.1007_s10878-021-00738-w
    DOI: 10.1007/s10878-021-00738-w
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10878-021-00738-w
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s10878-021-00738-w?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.
    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. 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. 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.
    4. Nie, Kairui & Ma, Yingbin & Sidorowicz, Elżbieta, 2023. "(Strong) Proper vertex connection of some digraphs," Applied Mathematics and Computation, Elsevier, vol. 458(C).
    5. 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.
    6. 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.
    7. Ma, Yingbin & Zhang, Xiaoxue, 2023. "Graphs with (strong) proper connection numbers m−3 and m−4," Applied Mathematics and Computation, Elsevier, vol. 445(C).
    8. 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.

    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:spr:jcomop:v:42:y:2021:i:1:d:10.1007_s10878-021-00738-w. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.