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On the fault-tolerant metric dimension of convex polytopes

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  • Raza, Hassan
  • Hayat, Sakander
  • Pan, Xiang-Feng

Abstract

A convex polytopes is a polytope that is also a convex set of points in the n-dimensional Euclidean space Rn. By preserving the same adjacency relation between vertices of a convex polytope, its graph is constructed. The metric dimension problem has been extensively studied for convex polytopes and other families of graphs. In this paper, we study the fault-tolerant metric dimension problem for convex polytopes. By using a relation between resolving sets and fault-tolerant resolving sets of graphs, we prove that certain infinite families of convex polytopes are the families of graphs with constant fault-tolerant metric dimension. We conclude the paper with some open problems.

Suggested Citation

  • Raza, Hassan & Hayat, Sakander & Pan, Xiang-Feng, 2018. "On the fault-tolerant metric dimension of convex polytopes," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 172-185.
    • Handle: RePEc:eee:apmaco:v:339:y:2018:i:c:p:172-185
    DOI: 10.1016/j.amc.2018.07.010
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    References listed on IDEAS

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    1. Gao, Wei & Farahani, Mohammad Reza & Wang, Shaohui & Husin, Mohamad Nazri, 2017. "On the edge-version atom-bond connectivity and geometric arithmetic indices of certain graph operations," Applied Mathematics and Computation, Elsevier, vol. 308(C), pages 11-17.
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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).
    2. Hassan Raza & Sakander Hayat & Muhammad Imran & Xiang-Feng Pan, 2019. "Fault-Tolerant Resolvability and Extremal Structures of Graphs," Mathematics, MDPI, vol. 7(1), pages 1-19, January.
    3. Sakander Hayat & Asad Khan & Yubin Zhong, 2022. "On Resolvability- and Domination-Related Parameters of Complete Multipartite Graphs," Mathematics, MDPI, vol. 10(11), pages 1-16, May.
    4. Muhammad Azeem & Muhammad Kamran Jamil & Yilun Shang, 2023. "Notes on the Localization of Generalized Hexagonal Cellular Networks," Mathematics, MDPI, vol. 11(4), pages 1-15, February.
    5. Hassan Raza, 2021. "Computing Open Locating-Dominating Number of Some Rotationally-Symmetric Graphs," Mathematics, MDPI, vol. 9(12), pages 1-12, June.

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