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Determining the edge metric dimension of the generalized Petersen graph P(n, 3)

Author

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  • David G. L. Wang

    (School of Mathematics and Statistics, Beijing Institute of Technology
    Beijing Key Laboratory on MCAACI, Beijing Institute of Technology
    Key Laboratory of Mathematical Theory and Computation in Information Security, Ministry of Industry and Information Technology)

  • Monica M. Y. Wang

    (School of Mathematics and Statistics, Beijing Institute of Technology)

  • Shiqiang Zhang

    (Department of Computing, Imperial College London)

Abstract

It is known that the problem of computing the edge dimension of a graph is NP-hard, and that the edge dimension of any generalized Petersen graph P(n, k) is at least 3. We prove that the graph P(n, 3) has edge dimension 4 for $$n\ge 11$$ n ≥ 11 , by showing semi-combinatorially the nonexistence of an edge resolving set of order 3 and by constructing explicitly an edge resolving set of order 4.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jcomop:v:43:y:2022:i:2:d:10.1007_s10878-021-00780-8
    DOI: 10.1007/s10878-021-00780-8
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    References listed on IDEAS

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    1. Amir Daneshgar & Meysam Madani, 2017. "On the odd girth and the circular chromatic number of generalized Petersen graphs," Journal of Combinatorial Optimization, Springer, vol. 33(3), pages 897-923, April.
    2. Kelenc, Aleksander & Kuziak, Dorota & Taranenko, Andrej & G. Yero, Ismael, 2017. "Mixed metric dimension of graphs," Applied Mathematics and Computation, Elsevier, vol. 314(C), pages 429-438.
    3. Yang, Zixuan & Wu, Baoyindureng, 2018. "Strong edge chromatic index of the generalized Petersen graphs," Applied Mathematics and Computation, Elsevier, vol. 321(C), pages 431-441.
    4. Guangjun Xu & Liying Kang, 2011. "On the power domination number of the generalized Petersen graphs," Journal of Combinatorial Optimization, Springer, vol. 22(2), pages 282-291, August.
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    Cited by:

    1. Enqiang Zhu & Shaoxiang Peng & Chanjuan Liu, 2022. "Identifying the Exact Value of the Metric Dimension and Edge Dimension of Unicyclic Graphs," Mathematics, MDPI, vol. 10(19), pages 1-14, September.

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