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Minimal Doubly Resolving Sets of Some Classes of Convex Polytopes

Author

Listed:
  • Muhammad Ahmad
  • Dalal Alrowaili
  • Zohaib Zahid
  • Imran Siddique
  • Aiyared Iampan

Abstract

Source localization is one of the most challenging problems in complex networks. Monitoring and controlling complex networks is of great interest for understanding different types of systems, such as biological, technological, and complex physical systems. Modern research has made great developments in identifying sensors through which we can monitor or control complex systems. For this task, we choose a set of sensors with the smallest possible size so that the source may be identified. The problem of locating the source of an epidemic in a network is equivalent to the problem of finding the minimal doubly resolving sets (MDRSs) in a network. In this paper, we calculate the minimal doubly resolving sets (MDRSs) of some classes of convex polytopes in order to compute their double metric dimension (DMD).

Suggested Citation

  • Muhammad Ahmad & Dalal Alrowaili & Zohaib Zahid & Imran Siddique & Aiyared Iampan, 2022. "Minimal Doubly Resolving Sets of Some Classes of Convex Polytopes," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:jjmath:v:2022:y:2022:i:1:n:1818734
    DOI: 10.1155/2022/1818734
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    References listed on IDEAS

    as
    1. Jia-Bao Liu & Zohaib Zahid & Ruby Nasir & Waqas Nazeer, 2018. "Edge Version of Metric Dimension and Doubly Resolving Sets of the Necklace Graph," Mathematics, MDPI, vol. 6(11), pages 1-10, November.
    2. Jia-Bao Liu & Ali Zafari, 2020. "Computing Minimal Doubly Resolving Sets and the Strong Metric Dimension of the Layer Sun Graph and the Line Graph of the Layer Sun Graph," Complexity, Hindawi, vol. 2020, pages 1-8, September.
    3. Jia-Bao Liu & Ali Zafari & Hassan Zarei, 2020. "Metric Dimension, Minimal Doubly Resolving Sets, and the Strong Metric Dimension for Jellyfish Graph and Cocktail Party Graph," Complexity, Hindawi, vol. 2020, pages 1-7, May.
    4. Liying Pan & Muhammad Ahmad & Zohaib Zahid & Sohail Zafar & Kenan Yildirim, 2021. "Computation of the Double Metric Dimension in Convex Polytopes," Journal of Mathematics, Hindawi, vol. 2021, pages 1-11, October.
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    Cited by:

    1. Muhammad Ahmad & Dalal Alrowaili & Rifaqat Ali & Zohaib Zahid & Imran Siddique, 2022. "Double Metric Resolvability in Convex Polytopes," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).

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