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Fault-Tolerant Resolvability in Some Classes of Line Graphs

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  • Xuan Guo
  • Muhammad Faheem
  • Zohaib Zahid
  • Waqas Nazeer
  • Jingjng Li

Abstract

Fault tolerance is the characteristic of a system that permits it to carry on its intended operations in case of the failure of one of its units. Such a system is known as the fault-tolerant self-stable system. In graph theory, if we remove any vertex in a resolving set, then the resulting set is also a resolving set, called the fault-tolerant resolving set, and its minimum cardinality is called the fault-tolerant metric dimension. In this paper, we determine the fault-tolerant resolvability in line graphs. As a main result, we computed the fault-tolerant metric dimension of line graphs of necklace and prism graphs (2010 Mathematics Subject Classification: 05C78).

Suggested Citation

  • Xuan Guo & Muhammad Faheem & Zohaib Zahid & Waqas Nazeer & Jingjng Li, 2020. "Fault-Tolerant Resolvability in Some Classes of Line Graphs," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-8, September.
    • Handle: RePEc:hin:jnlmpe:1436872
    DOI: 10.1155/2020/1436872
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    Cited by:

    1. Arulperumjothi, M. & Klavžar, Sandi & Prabhu, S., 2023. "Redefining fractal cubic networks and determining their metric dimension and fault-tolerant metric dimension," Applied Mathematics and Computation, Elsevier, vol. 452(C).

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