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Metric dimensions of generalized Sierpiński graphs over squares

Author

Listed:
  • Prabhu, S.
  • Janany, T. Jenifer
  • Klavžar, Sandi

Abstract

Metric dimension is a valuable parameter that helps address problems related to network design, localization, and information retrieval by identifying the minimum number of landmarks required to uniquely determine distances between vertices in a graph. Generalized Sierpiński graphs represent a captivating class of fractal-inspired networks that have gained prominence in various scientific disciplines and practical applications. Their fractal nature has also found relevance in antenna design, image compression, and the study of porous materials. The hypercube is a prevalent interconnection network architecture known for its symmetry, vertex transitivity, regularity, recursive structure, high connectedness, and simple routing. Various variations of hypercubes have emerged in literature to meet the demands of practical applications. Sometimes, they are the spanning subgraphs of it. This study examines the generalized Sierpiński graphs over C4, which are spanning subgraphs of hypercubes and determines the metric dimension and their variants. This is in contrast to hypercubes, where these properties are inherently complicated. Along the way, the role of twin vertices in the theory of metric dimensions is further elaborated.

Suggested Citation

  • Prabhu, S. & Janany, T. Jenifer & Klavžar, Sandi, 2025. "Metric dimensions of generalized Sierpiński graphs over squares," Applied Mathematics and Computation, Elsevier, vol. 505(C).
    • Handle: RePEc:eee:apmaco:v:505:y:2025:i:c:s0096300325002541
    DOI: 10.1016/j.amc.2025.129528
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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. Knor, Martin & Majstorović, Snježana & Masa Toshi, Aoden Teo & Škrekovski, Riste & Yero, Ismael G., 2021. "Graphs with the edge metric dimension smaller than the metric dimension," Applied Mathematics and Computation, Elsevier, vol. 401(C).
    3. Imran, Muhammad & Sabeel-e-Hafi, & Gao, Wei & Reza Farahani, Mohammad, 2017. "On topological properties of sierpinski networks," Chaos, Solitons & Fractals, Elsevier, vol. 98(C), pages 199-204.
    4. Changcheng Wei & Muhammad Salman & Syed Shahzaib & Masood Ur Rehman & Juanyan Fang & M. Irfan Uddin, 2021. "Classes of Planar Graphs with Constant Edge Metric Dimension," Complexity, Hindawi, vol. 2021, pages 1-10, April.
    5. Yuezhong Zhang & Suogang Gao, 2020. "On the edge metric dimension of convex polytopes and its related graphs," Journal of Combinatorial Optimization, Springer, vol. 39(2), pages 334-350, February.
    6. David G. L. Wang & Monica M. Y. Wang & Shiqiang Zhang, 2022. "Determining the edge metric dimension of the generalized Petersen graph P(n, 3)," Journal of Combinatorial Optimization, Springer, vol. 43(2), pages 460-496, March.
    7. 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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