IDEAS home Printed from https://ideas.repec.org/a/hin/jnddns/4531958.html
   My bibliography  Save this article

The Metric Dimension of Some Generalized Petersen Graphs

Author

Listed:
  • Zehui Shao
  • S. M. Sheikholeslami
  • Pu Wu
  • Jia-Biao Liu

Abstract

The distance between two distinct vertices and in a graph is the length of a shortest -path in . For an ordered subset of vertices and a vertex in , the code of with respect to is the ordered -tuple . The set is a resolving set for if every two vertices of have distinct codes. The metric dimension of is the minimum cardinality of a resolving set of . In this paper, we first extend the results of the metric dimension of and and study bounds on the metric dimension of the families of the generalized Petersen graphs and . The obtained results mean that these families of graphs have constant metric dimension.

Suggested Citation

  • Zehui Shao & S. M. Sheikholeslami & Pu Wu & Jia-Biao Liu, 2018. "The Metric Dimension of Some Generalized Petersen Graphs," Discrete Dynamics in Nature and Society, Hindawi, vol. 2018, pages 1-10, August.
    • Handle: RePEc:hin:jnddns:4531958
    DOI: 10.1155/2018/4531958
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/DDNS/2018/4531958.pdf
    Download Restriction: no
    File URL: http://downloads.hindawi.com/journals/DDNS/2018/4531958.xml
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2018/4531958?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
    ---><---

    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.

    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:hin:jnddns:4531958. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Mohamed Abdelhakeem (email available below). General contact details of provider: https://www.hindawi.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.