IDEAS home Printed from https://ideas.repec.org/a/spr/jcomop/v14y2007i2d10.1007_s10878-007-9057-5.html
   My bibliography  Save this article

L(j,k)- and circular L(j,k)-labellings for the products of complete graphs

Author

Listed:
  • Peter Che Bor Lam

    (Hong Kong Baptist University)

  • Wensong Lin

    (Hong Kong Baptist University
    Southeast University)

  • Jianzhuan Wu

    (Southeast University)

Abstract

Let j and k be two positive integers with j≥k. An L(j,k)-labelling of a graph G is an assignment of nonnegative integers to the vertices of G such that the difference between labels of any two adjacent vertices is at least j, and the difference between labels of any two vertices that are at distance two apart is at least k. The minimum range of labels over all L(j,k)-labellings of a graph G is called the λ j,k -number of G, denoted by λ j,k (G). A σ(j,k)-circular labelling with span m of a graph G is a function f:V(G)→{0,1,…,m−1} such that |f(u)−f(v)| m ≥j if u and v are adjacent; and |f(u)−f(v)| m ≥k if u and v are at distance two apart, where |x| m =min {|x|,m−|x|}. The minimum m such that there exists a σ(j,k)-circular labelling with span m for G is called the σ j,k -number of G and denoted by σ j,k (G). The λ j,k -numbers of Cartesian products of two complete graphs were determined by Georges, Mauro and Stein ((2000) SIAM J Discret Math 14:28–35). This paper determines the λ j,k -numbers of direct products of two complete graphs and the σ j,k -numbers of direct products and Cartesian products of two complete graphs.

Suggested Citation

  • Peter Che Bor Lam & Wensong Lin & Jianzhuan Wu, 2007. "L(j,k)- and circular L(j,k)-labellings for the products of complete graphs," Journal of Combinatorial Optimization, Springer, vol. 14(2), pages 219-227, October.
    • Handle: RePEc:spr:jcomop:v:14:y:2007:i:2:d:10.1007_s10878-007-9057-5
    DOI: 10.1007/s10878-007-9057-5
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10878-007-9057-5
    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/s10878-007-9057-5?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.

    Citations

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


    Cited by:

    1. Wensong Lin & Jianzhuan Wu, 2013. "Distance two edge labelings of lattices," Journal of Combinatorial Optimization, Springer, vol. 25(4), pages 661-679, May.

    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:14:y:2007:i:2:d:10.1007_s10878-007-9057-5. 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: 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.