IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i2p351-d1030140.html
   My bibliography  Save this article

Double Roman Domination: A Survey

Author

Listed:
  • Darja Rupnik Poklukar

    (Faculty of Mechanical Engineering, University of Ljubljana, Aškerčeva 6, 1000 Ljubljana, Slovenia)

  • Janez Žerovnik

    (Faculty of Mechanical Engineering, University of Ljubljana, Aškerčeva 6, 1000 Ljubljana, Slovenia)

Abstract

Since 2016, when the first paper of the double Roman domination appeared, the topic has received considerable attention in the literature. We survey known results on double Roman domination and some variations of the double Roman domination, and a list of open questions and conjectures is provided.

Suggested Citation

  • Darja Rupnik Poklukar & Janez Žerovnik, 2023. "Double Roman Domination: A Survey," Mathematics, MDPI, vol. 11(2), pages 1-20, January.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:2:p:351-:d:1030140
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/2/351/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/2/351/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Huiqin Jiang & Pu Wu & Zehui Shao & Yongsheng Rao & Jia-Bao Liu, 2018. "The Double Roman Domination Numbers of Generalized Petersen Graphs P ( n , 2)," Mathematics, MDPI, vol. 6(10), pages 1-11, October.
    2. Hong Yang & Xiaoqing Zhou, 2020. "Some Properties of Double Roman Domination," Discrete Dynamics in Nature and Society, Hindawi, vol. 2020, pages 1-5, August.
    3. Yue, Jun & Wei, Meiqin & Li, Min & Liu, Guodong, 2018. "On the double Roman domination of graphs," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 669-675.
    4. J. Amjadi & S. Nazari-Moghaddam & S. M. Sheikholeslami & L. Volkmann, 2018. "An upper bound on the double Roman domination number," Journal of Combinatorial Optimization, Springer, vol. 36(1), pages 81-89, July.
    5. S. Banerjee & Michael A. Henning & D. Pradhan, 2020. "Algorithmic results on double Roman domination in graphs," Journal of Combinatorial Optimization, Springer, vol. 39(1), pages 90-114, January.
    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. Ana Klobučar Barišić & Robert Manger, 2024. "Solving the minimum-cost double Roman domination problem," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 32(3), pages 793-817, September.

    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. Zehui Shao & Rija Erveš & Huiqin Jiang & Aljoša Peperko & Pu Wu & Janez Žerovnik, 2021. "Double Roman Graphs in P (3 k , k )," Mathematics, MDPI, vol. 9(4), pages 1-18, February.
    2. Samadi, B. & Soltankhah, N. & Abdollahzadeh Ahangar, H. & Chellali, M. & Mojdeh, D.A. & Sheikholeslami, S.M. & Valenzuela-Tripodoro, J.C., 2023. "Restrained condition on double Roman dominating functions," Applied Mathematics and Computation, Elsevier, vol. 438(C).
    3. S. Banerjee & Michael A. Henning & D. Pradhan, 2020. "Algorithmic results on double Roman domination in graphs," Journal of Combinatorial Optimization, Springer, vol. 39(1), pages 90-114, January.
    4. Ana Klobučar Barišić & Robert Manger, 2024. "Solving the minimum-cost double Roman domination problem," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 32(3), pages 793-817, September.
    5. Enrico Enriquez & Grace Estrada & Carmelita Loquias & Reuella J Bacalso & Lanndon Ocampo, 2021. "Domination in Fuzzy Directed Graphs," Mathematics, MDPI, vol. 9(17), pages 1-14, September.
    6. Liu, Xiaoxiao & Sun, Shiwen & Wang, Jiawei & Xia, Chengyi, 2019. "Onion structure optimizes attack robustness of interdependent networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 535(C).
    7. Banerjee, S. & Henning, Michael A. & Pradhan, D., 2021. "Perfect Italian domination in cographs," Applied Mathematics and Computation, Elsevier, vol. 391(C).
    8. Frank Werner, 2019. "Discrete Optimization: Theory, Algorithms, and Applications," Mathematics, MDPI, vol. 7(5), pages 1-4, May.
    9. Ma, Yuede & Cai, Qingqiong & Yao, Shunyu, 2019. "Integer linear programming models for the weighted total domination problem," Applied Mathematics and Computation, Elsevier, vol. 358(C), pages 146-150.
    10. Peng Li, 2024. "The k-th Roman domination problem is polynomial on interval graphs," Journal of Combinatorial Optimization, Springer, vol. 48(3), pages 1-14, October.
    11. Ching-Chi Lin & Cheng-Yu Hsieh & Ta-Yu Mu, 2022. "A linear-time algorithm for weighted paired-domination on block graphs," Journal of Combinatorial Optimization, Springer, vol. 44(1), pages 269-286, August.
    12. Hao Guan & Waheed Ahmad Khan & Amna Fida & Khadija Ali & Jana Shafi & Aysha Khan, 2024. "Dominations in Intutionistic Fuzzy Directed Graphs with Applications towards Influential Graphs," Mathematics, MDPI, vol. 12(6), pages 1-14, March.
    13. Bermudo, Sergio & Higuita, Robinson A. & Rada, Juan, 2020. "Domination in hexagonal chains," Applied Mathematics and Computation, Elsevier, vol. 369(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:gam:jmathe:v:11:y:2023:i:2:p:351-:d:1030140. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.