IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i14p2445-d862037.html
   My bibliography  Save this article

On the Characterization of a Minimal Resolving Set for Power of Paths

Author

Listed:
  • Laxman Saha

    (Department of Mathematics, Balurghat College, Dakshin Dinajpur, Balurghat 733101, India)

  • Mithun Basak

    (Department of Mathematics, Balurghat College, Dakshin Dinajpur, Balurghat 733101, India)

  • Kalishankar Tiwary

    (Department of Mathematics, Raiganj University, Raiganj 733134, India)

  • Kinkar Chandra Das

    (Department of Mathematics, Sungkyunkwan University, Suwon 16419, Korea)

  • Yilun Shang

    (Department of Computer and Information Sciences, Northumbria University, Newcastle NE1 8ST, UK)

Abstract

For a simple connected graph G = ( V , E ) , an ordered set W ⊆ V , is called a resolving set of G if for every pair of two distinct vertices u and v , there is an element w in W such that d ( u , w ) ≠ d ( v , w ) . A metric basis of G is a resolving set of G with minimum cardinality. The metric dimension of G is the cardinality of a metric basis and it is denoted by β ( G ) . In this article, we determine the metric dimension of power of finite paths and characterize all metric bases for the same.

Suggested Citation

  • Laxman Saha & Mithun Basak & Kalishankar Tiwary & Kinkar Chandra Das & Yilun Shang, 2022. "On the Characterization of a Minimal Resolving Set for Power of Paths," Mathematics, MDPI, vol. 10(14), pages 1-13, July.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:14:p:2445-:d:862037
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/14/2445/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/14/2445/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Jun Guo & Kaishun Wang & Fenggao Li, 2013. "Metric dimension of some distance-regular graphs," Journal of Combinatorial Optimization, Springer, vol. 26(1), pages 190-197, July.
    2. Laxman Saha & Rupen Lama & Kalishankar Tiwary & Kinkar Chandra Das & Yilun Shang, 2022. "Fault-Tolerant Metric Dimension of Circulant Graphs," Mathematics, MDPI, vol. 10(1), pages 1-16, January.
    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. 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.
    2. Laxman Saha & Rupen Lama & Bapan Das & Avishek Adhikari & Kinkar Chandra Das, 2023. "Optimal Fault-Tolerant Resolving Set of Power Paths," Mathematics, MDPI, vol. 11(13), pages 1-18, June.
    3. Laxman Saha & Bapan Das & Kalishankar Tiwary & Kinkar Chandra Das & Yilun Shang, 2023. "Optimal Multi-Level Fault-Tolerant Resolving Sets of Circulant Graph C ( n : 1, 2)," Mathematics, MDPI, vol. 11(8), pages 1-16, April.

    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. Muhammad Azeem & Muhammad Kamran Jamil & Yilun Shang, 2023. "Notes on the Localization of Generalized Hexagonal Cellular Networks," Mathematics, MDPI, vol. 11(4), pages 1-15, February.
    2. Laxman Saha & Bapan Das & Kalishankar Tiwary & Kinkar Chandra Das & Yilun Shang, 2023. "Optimal Multi-Level Fault-Tolerant Resolving Sets of Circulant Graph C ( n : 1, 2)," Mathematics, MDPI, vol. 11(8), pages 1-16, April.

    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:gam:jmathe:v:10:y:2022:i:14:p:2445-:d:862037. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.