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Double Metric Resolvability in Convex Polytopes

Author

Listed:
  • Muhammad Ahmad
  • Dalal Alrowaili
  • Rifaqat Ali
  • Zohaib Zahid
  • Imran Siddique

Abstract

Nowadays, the study of source localization in complex networks is a critical issue. Localization of the source has been investigated using a variety of feasible models. To identify the source of a network’s diffusion, it is necessary to find a vertex from which the observed diffusion spreads. Detecting the source of a virus in a network is equivalent to finding the minimal doubly resolving set (MDRS) in a network. This paper calculates the doubly resolving sets (DRSs) for certain convex polytope structures to calculate their double metric dimension (DMD). It is concluded that the cardinality of MDRSs for these convex polytopes is finite and constant.

Suggested Citation

  • 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).
    • Handle: RePEc:wly:jjmath:v:2022:y:2022:i:1:n:5884924
    DOI: 10.1155/2022/5884924
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    References listed on IDEAS

    as
    1. András Sebő & Eric Tannier, 2004. "On Metric Generators of Graphs," Mathematics of Operations Research, INFORMS, vol. 29(2), pages 383-393, May.
    2. Muhammad Ahmad & Dalal Alrowaili & Zohaib Zahid & Imran Siddique & Aiyared Iampan & Gohar Ali, 2022. "Minimal Doubly Resolving Sets of Some Classes of Convex Polytopes," Journal of Mathematics, Hindawi, vol. 2022, pages 1-13, February.
    3. 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.
    4. 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).
    5. 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.
    6. 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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