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Survey on Roman {2}-Domination

Author

Listed:
  • Ahlam Almulhim

    (Department of Mathematics and Statistics, College of Science, King Faisal University, P.O. Box 400, Al-Ahsa 31982, Saudi Arabia)

  • Bana Al Subaiei

    (Department of Mathematics and Statistics, College of Science, King Faisal University, P.O. Box 400, Al-Ahsa 31982, Saudi Arabia)

  • Saiful Rahman Mondal

    (Department of Mathematics and Statistics, College of Science, King Faisal University, P.O. Box 400, Al-Ahsa 31982, Saudi Arabia)

Abstract

The notion of Roman { 2 } -domination was introduced in 2016 as a variant of Roman domination, a concept inspired by a defending strategy used by the emperor Constantine (272–337 AD) to protect the Roman Empire. Since then, a considerable number of papers on Roman { 2 } -domination and its variants have been published. In this paper, we survey published results on Roman { 2 } -domination as well as the main findings on Roman { 2 } -domination variants found in the literature. A list of open problems related to this notion and its variants are also given.

Suggested Citation

  • Ahlam Almulhim & Bana Al Subaiei & Saiful Rahman Mondal, 2024. "Survey on Roman {2}-Domination," Mathematics, MDPI, vol. 12(17), pages 1-20, September.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:17:p:2771-:d:1473357
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    References listed on IDEAS

    as
    1. Zepeng Li & Zehui Shao & Jin Xu, 2018. "Weak {2}-domination number of Cartesian products of cycles," Journal of Combinatorial Optimization, Springer, vol. 35(1), pages 75-85, January.
    2. M. Kheibari & H. Abdollahzadeh Ahangar & R. Khoeilar & S. M. Sheikholeslami & Ahmet Sinan Cevik, 2021. "Total Roman 2-Reinforcement of Graphs," Journal of Mathematics, Hindawi, vol. 2021, pages 1-7, April.
    3. Chun-Hung Liu & Gerard J. Chang, 2013. "Roman domination on strongly chordal graphs," Journal of Combinatorial Optimization, Springer, vol. 26(3), pages 608-619, October.
    4. Kijung Kim, 2020. "The Italian Domination Numbers of Some Products of Directed Cycles," Mathematics, MDPI, vol. 8(9), pages 1-6, September.
    5. M. Dettlaff & M. Lemańska & J. A. Rodríguez-Velázquez, 2021. "Secure Italian domination in graphs," Journal of Combinatorial Optimization, Springer, vol. 41(1), pages 56-72, January.
    Full references (including those not matched with items on IDEAS)

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