IDEAS home Printed from https://ideas.repec.org/a/spr/jcomop/v43y2022i2d10.1007_s10878-021-00780-8.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10878-021-00780-8
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10878-021-00780-8?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Ou Sun & Neng Fan, 2019. "Solving the multistage PMU placement problem by integer programming and equivalent network design model," Journal of Global Optimization, Springer, vol. 74(3), pages 477-493, July.
    2. Lily Chen & Shumei Chen & Ren Zhao & Xiangqian Zhou, 2020. "The strong chromatic index of graphs with edge weight eight," Journal of Combinatorial Optimization, Springer, vol. 40(1), pages 227-233, July.
    3. Sedlar, Jelena & Škrekovski, Riste, 2021. "Bounds on metric dimensions of graphs with edge disjoint cycles," Applied Mathematics and Computation, Elsevier, vol. 396(C).
    4. 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.
    5. Martin Knor & Jelena Sedlar & Riste Škrekovski, 2022. "Remarks on the Vertex and the Edge Metric Dimension of 2-Connected Graphs," Mathematics, MDPI, vol. 10(14), pages 1-16, July.
    6. Juan Wang & Lianying Miao & Yunlong Liu, 2019. "Characterization of n -Vertex Graphs of Metric Dimension n − 3 by Metric Matrix," Mathematics, MDPI, vol. 7(5), pages 1-13, May.
    7. Chao Wang & Lei Chen & Changhong Lu, 2016. "$$k$$ k -Power domination in block graphs," Journal of Combinatorial Optimization, Springer, vol. 31(2), pages 865-873, February.
    8. Dorota Kuziak, 2020. "The Strong Resolving Graph and the Strong Metric Dimension of Cactus Graphs," Mathematics, MDPI, vol. 8(8), pages 1-14, August.
    9. Sedlar, Jelena & Škrekovski, Riste, 2022. "Metric dimensions vs. cyclomatic number of graphs with minimum degree at least two," Applied Mathematics and Computation, Elsevier, vol. 427(C).
    10. Chung-Shou Liao, 2016. "Power domination with bounded time constraints," Journal of Combinatorial Optimization, Springer, vol. 31(2), pages 725-742, February.
    11. Nie, Kairui & Xu, Kexiang, 2023. "Mixed metric dimension of some graphs," Applied Mathematics and Computation, Elsevier, vol. 442(C).
    12. Sedlar, Jelena & Škrekovski, Riste, 2021. "Extremal mixed metric dimension with respect to the cyclomatic number," Applied Mathematics and Computation, Elsevier, vol. 404(C).
    13. Ming Chen & Lianying Miao & Shan Zhou, 2020. "Strong Edge Coloring of Generalized Petersen Graphs," Mathematics, MDPI, vol. 8(8), pages 1-12, August.
    14. Asad Khan & Ghulam Haidar & Naeem Abbas & Murad Ul Islam Khan & Azmat Ullah Khan Niazi & Asad Ul Islam Khan, 2023. "Metric Dimensions of Bicyclic Graphs," Mathematics, MDPI, vol. 11(4), pages 1-17, February.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:jcomop:v:43:y:2022:i:2:d:10.1007_s10878-021-00780-8. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.