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Fault-Tolerant Resolvability in Some Classes of Subdivision Graphs

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  • Muhammad Faheem
  • Zohaib Zahid
  • Dalal Alrowaili
  • Imran Siddique
  • Aiyared Iampan
  • Gul Rahmat

Abstract

The concept of resolving sets (RSs) and metric dimension (MD) invariants have a wide range of applications in robot navigation, computer networks, and chemical structure. RS has been used as a sensor in an indoor positioning system to find an interrupter. Many terminologies in machine learning have also been used to diagnose the interrupter in the systems of marine and gas turbines using sensory data. We proposed a fault-tolerant self-stable system that allows for the detection of an interrupter even if one of the sensors in the chain fails. If the elimination of any element from a RS is still a RS, then the RS is considered as a fault-tolerant resolving set (FTRS), and the fault-tolerant metric dimension (FTMD) is its minimum cardinality. In this paper, we calculated the FTMD of the subdivision graphs of the necklace and prism graphs. We also found that this invariant has constant values for both graphs.

Suggested Citation

  • Muhammad Faheem & Zohaib Zahid & Dalal Alrowaili & Imran Siddique & Aiyared Iampan & Gul Rahmat, 2022. "Fault-Tolerant Resolvability in Some Classes of Subdivision Graphs," Journal of Mathematics, Hindawi, vol. 2022, pages 1-15, February.
    • Handle: RePEc:hin:jjmath:5784800
    DOI: 10.1155/2022/5784800
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