IDEAS home Printed from https://ideas.repec.org/a/spr/jcomop/v26y2013i1d10.1007_s10878-012-9459-x.html
   My bibliography  Save this article

Metric dimension of some distance-regular graphs

Author

Listed:
  • Jun Guo

    (Langfang Teachers’ College)

  • Kaishun Wang

    (Beijing Normal University)

  • Fenggao Li

    (Hunan Institute of Science and Technology)

Abstract

A resolving set of a graph is a set of vertices with the property that the list of distances from any vertex to those in the set uniquely identifies that vertex. In this paper, we construct a resolving set of Johnson graphs, doubled Odd graphs, doubled Grassmann graphs and twisted Grassmann graphs, respectively, and obtain the upper bounds on the metric dimension of these graphs.

Suggested Citation

  • 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.
  • Handle: RePEc:spr:jcomop:v:26:y:2013:i:1:d:10.1007_s10878-012-9459-x
    DOI: 10.1007/s10878-012-9459-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10878-012-9459-x
    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/s10878-012-9459-x?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. András Sebő & Eric Tannier, 2004. "On Metric Generators of Graphs," Mathematics of Operations Research, INFORMS, vol. 29(2), pages 383-393, May.
    2. van Dam, E.R. & Koolen, J.H., 2004. "A New Family of Distance-Regular Graphs with Unbounded Diameter," Discussion Paper 2004-116, Tilburg University, Center for Economic Research.
    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. 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.

    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. van Dam, E.R., 2008. "The spectral excess theorem for distance-regular graphs : A global (over)view," Other publications TiSEM 35daf99b-ad28-4e21-8b1f-6, Tilburg University, School of Economics and Management.
    2. Michael Hallaway & Cong X. Kang & Eunjeong Yi, 2014. "On metric dimension of permutation graphs," Journal of Combinatorial Optimization, Springer, vol. 28(4), pages 814-826, November.
    3. Ismael González Yero, 2020. "The Simultaneous Strong Resolving Graph and the Simultaneous Strong Metric Dimension of Graph Families," Mathematics, MDPI, vol. 8(1), pages 1-11, January.
    4. Dalfo, C. & van Dam, E.R. & Fiol, M.A., 2011. "On perturbations of almost distance-regular graphs," Other publications TiSEM 27186838-0516-45bb-8367-6, Tilburg University, School of Economics and Management.
    5. van Dam, E.R. & Haemers, W.H., 2007. "Developments on Spectral Characterizations of Graphs," Discussion Paper 2007-33, Tilburg University, Center for Economic Research.
    6. González, Antonio & Hernando, Carmen & Mora, Mercè, 2018. "Metric-locating-dominating sets of graphs for constructing related subsets of vertices," Applied Mathematics and Computation, Elsevier, vol. 332(C), pages 449-456.
    7. Sedlar, Jelena & Škrekovski, Riste, 2021. "Bounds on metric dimensions of graphs with edge disjoint cycles," Applied Mathematics and Computation, Elsevier, vol. 396(C).
    8. van Dam, E.R. & Haemers, W.H. & Koolen, J.H. & Spence, E., 2005. "Characterizing Distance-Regularity of Graphs by the Spectrum," Discussion Paper 2005-19, Tilburg University, Center for Economic Research.
    9. Abiad Monge, Aida, 2015. "Spectral characterizations of graphs," Other publications TiSEM 047213fe-66b3-4494-a7e0-c, Tilburg University, School of Economics and Management.
    10. Knor, Martin & Majstorović, Snježana & Masa Toshi, Aoden Teo & Škrekovski, Riste & Yero, Ismael G., 2021. "Graphs with the edge metric dimension smaller than the metric dimension," Applied Mathematics and Computation, Elsevier, vol. 401(C).
    11. Mladenović, Nenad & Kratica, Jozef & Kovačević-Vujčić, Vera & Čangalović, Mirjana, 2012. "Variable neighborhood search for metric dimension and minimal doubly resolving set problems," European Journal of Operational Research, Elsevier, vol. 220(2), pages 328-337.
    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. 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.
    14. Yero, Ismael G. & Estrada-Moreno, Alejandro & Rodríguez-Velázquez, Juan A., 2017. "Computing the k-metric dimension of graphs," Applied Mathematics and Computation, Elsevier, vol. 300(C), pages 60-69.
    15. Sunny Kumar Sharma & Vijay Kumar Bhat, 2022. "On metric dimension of plane graphs with $$\frac{m}{2}$$ m 2 number of 10 sided faces," Journal of Combinatorial Optimization, Springer, vol. 44(3), pages 1433-1458, October.
    16. 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.
    17. Abiad, Aida & D'haeseleer, Jozefien & Haemers, Willem H. & Simoens, Robin, 2023. "Cospectral Mates for Generalized Johnson and Grassmann Graphs," Other publications TiSEM a7bfd196-24a9-47fc-a96f-9, Tilburg University, School of Economics and Management.
    18. van Dam, E.R. & Haemers, W.H., 2007. "Developments on Spectral Characterizations of Graphs," Other publications TiSEM 3827c785-7b51-4bcd-aea3-f, Tilburg University, School of Economics and Management.
    19. Ron Adar & Leah Epstein, 2017. "The k-metric dimension," Journal of Combinatorial Optimization, Springer, vol. 34(1), pages 1-30, July.
    20. Iztok Peterin & Gabriel Semanišin, 2021. "On the Maximal Shortest Paths Cover Number," Mathematics, MDPI, vol. 9(14), pages 1-10, July.

    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:26:y:2013:i:1:d:10.1007_s10878-012-9459-x. 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.