IDEAS home Printed from https://ideas.repec.org/a/wly/jijmms/v2025y2025i1n6660723.html

Local Metric and Partition Resolvability of Graphs With Applications

Author

Listed:
  • Kamran Azhar
  • Asim Nadeem
  • Yilun Shang

Abstract

The distance‐based graph parameters are being used extensively in the fields of chemistry, computer science, scheduling and in many operations’ management problems. The unique identification of vertices plays a key role in the computation of these parameters. The local versions of these parameters deal with adjacent vertices and, in this manner, provide more applicability. In this manuscript, the exact values of local metric dimension and local partition dimension of tadpole and necklace graphs have been computed. The article also discusses the application of a local metric basis in the optimal allocation of fire stations in a region.

Suggested Citation

  • Kamran Azhar & Asim Nadeem & Yilun Shang, 2025. "Local Metric and Partition Resolvability of Graphs With Applications," International Journal of Mathematics and Mathematical Sciences, John Wiley & Sons, vol. 2025(1).
    • Handle: RePEc:wly:jijmms:v:2025:y:2025:i:1:n:6660723
    DOI: 10.1155/ijmm/6660723
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/ijmm/6660723
    Download Restriction: no
    File URL: https://libkey.io/10.1155/ijmm/6660723?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
    ---><---

    References listed on IDEAS

    as
    1. 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.
    Full references (including those not matched with items on IDEAS)

    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. José Cáceres & Ignacio M. Pelayo, 2025. "Metric Locations in Pseudotrees: A Survey and New Results," Mathematics, MDPI, vol. 13(4), pages 1-28, February.
    2. Sedlar, Jelena & Škrekovski, Riste, 2021. "Bounds on metric dimensions of graphs with edge disjoint cycles," Applied Mathematics and Computation, Elsevier, vol. 396(C).
    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. 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.
    5. 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.
    6. Dorota Kuziak, 2020. "The Strong Resolving Graph and the Strong Metric Dimension of Cactus Graphs," Mathematics, MDPI, vol. 8(8), pages 1-14, August.
    7. Rashad Ismail & Asim Nadeem & Kamran Azhar, 2024. "Local Metric Resolvability of Generalized Petersen Graphs," Mathematics, MDPI, vol. 12(14), pages 1-14, July.
    8. 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.
    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. Nie, Kairui & Xu, Kexiang, 2023. "Mixed metric dimension of some graphs," Applied Mathematics and Computation, Elsevier, vol. 442(C).
    11. Sedlar, Jelena & Škrekovski, Riste, 2021. "Extremal mixed metric dimension with respect to the cyclomatic number," Applied Mathematics and Computation, Elsevier, vol. 404(C).
    12. 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.

    More about this item

    Statistics

    Access and download statistics

    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:wly:jijmms:v:2025:y:2025:i:1:n:6660723. 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: Wiley Content Delivery (email available below). General contact details of provider: https://onlinelibrary.wiley.com/journal/6396 .

    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.