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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
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    References listed on IDEAS

    as
    1. Hong Yang & Xiaoqing Zhou, 2020. "Some Properties of Double Roman Domination," Discrete Dynamics in Nature and Society, Hindawi, vol. 2020, pages 1-5, August.
    2. 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.
    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. 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.
    5. 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.
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    Citations

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    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.

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