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Redefining fractal cubic networks and determining their metric dimension and fault-tolerant metric dimension

Author

Listed:
  • Arulperumjothi, M.
  • Klavžar, Sandi
  • Prabhu, S.

Abstract

In network theory, distance parameters are crucial in analyzing structural aspects of the networks under investigation, including their symmetry, connectedness, and tendency to form clusters. To this end, the metric dimension and the fault-tolerant metric dimension are important distance invariants of networks. In this article, we consider fractal cubic networks, a variant of hypercubes. We first correct their definition from the seminal paper [Engineering Science and Technology, an International Journal 18 (2015) 32–41]. After that, we determine their metric dimension and fault-tolerant metric dimension, which is in striking contrast to the situation with hypercubes, where these invariants are intrinsically difficult.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:apmaco:v:452:y:2023:i:c:s0096300323002060
    DOI: 10.1016/j.amc.2023.128037
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    References listed on IDEAS

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    1. Prabhu, S. & Manimozhi, V. & Arulperumjothi, M. & Klavžar, Sandi, 2022. "Twin vertices in fault-tolerant metric sets and fault-tolerant metric dimension of multistage interconnection networks," Applied Mathematics and Computation, Elsevier, vol. 420(C).
    2. 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.
    3. 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.
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