IDEAS home Printed from https://ideas.repec.org/a/spr/jcomop/v27y2014i2d10.1007_s10878-012-9520-9.html
   My bibliography  Save this article

Circular L(j,k)-labeling number of direct product of path and cycle

Author

Listed:
  • Qiong Wu

    (Hong Kong Baptist University)

  • Wai Chee Shiu

    (Hong Kong Baptist University)

  • Pak Kiu Sun

    (Hong Kong Baptist University)

Abstract

Let j, k and m be positive numbers, a circular m-L(j,k)-labeling of a graph G is a function f:V(G)→[0,m) 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, where |a−b| m =min{|a−b|,m−|a−b|}. The minimum m such that there exist a circular m-L(j,k)-labeling of G is called the circular L(j,k)-labeling number of G and is denoted by σ j,k (G). In this paper, for any two positive numbers j and k with j≤k, we give some results about the circular L(j,k)-labeling number of direct product of path and cycle.

Suggested Citation

  • Qiong Wu & Wai Chee Shiu & Pak Kiu Sun, 2014. "Circular L(j,k)-labeling number of direct product of path and cycle," Journal of Combinatorial Optimization, Springer, vol. 27(2), pages 355-368, February.
    • Handle: RePEc:spr:jcomop:v:27:y:2014:i:2:d:10.1007_s10878-012-9520-9
    DOI: 10.1007/s10878-012-9520-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10878-012-9520-9
    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/s10878-012-9520-9?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. Jerrold R. Griggs & Xiaohua Teresa Jin, 2007. "Recent progress in mathematics and engineering on optimal graph labellings with distance conditions," Journal of Combinatorial Optimization, Springer, vol. 14(2), pages 249-257, October.
    2. Xiaohua Teresa Jin & Roger K. Yeh, 2005. "Graph distance‐dependent labeling related to code assignment in computer networks," Naval Research Logistics (NRL), John Wiley & Sons, vol. 52(2), pages 159-164, March.
    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. Wensong Lin, 2016. "On $$(s,t)$$ ( s , t ) -relaxed $$L(2,1)$$ L ( 2 , 1 ) -labeling of graphs," Journal of Combinatorial Optimization, Springer, vol. 31(1), pages 405-426, January.
    2. Wensong Lin & Benqiu Dai, 2015. "On $$(s,t)$$ ( s , t ) -relaxed $$L(2,1)$$ L ( 2 , 1 ) -labelings of the triangular lattice," Journal of Combinatorial Optimization, Springer, vol. 29(3), pages 655-669, April.
    3. Qiong Wu & Wai Chee Shiu & Pak Kiu Sun, 2016. "$$L(j,k)$$ L ( j , k ) -labeling number of Cartesian product of path and cycle," Journal of Combinatorial Optimization, Springer, vol. 31(2), pages 604-634, February.
    4. Xiaoling L. Zhang & Jianguo G. Qian, 2016. "$$L(p,q)$$ L ( p , q ) -labeling and integer tension of a graph embedded on torus," Journal of Combinatorial Optimization, Springer, vol. 31(1), pages 67-77, January.
    5. Jerrold R. Griggs & Xiaohua Teresa Jin, 2007. "Recent progress in mathematics and engineering on optimal graph labellings with distance conditions," Journal of Combinatorial Optimization, Springer, vol. 14(2), pages 249-257, October.
    6. Pu Zhang & Wensong Lin, 2014. "Multiple L(j,1)-labeling of the triangular lattice," Journal of Combinatorial Optimization, Springer, vol. 27(4), pages 695-710, May.
    7. Wensong Lin & Chenli Shen, 2018. "Channel assignment problem and n-fold t-separated $$L(j_1,j_2,\ldots ,j_m)$$ L ( j 1 , j 2 , … , j m ) -labeling of graphs," Journal of Combinatorial Optimization, Springer, vol. 35(4), pages 1147-1167, May.
    8. 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:27:y:2014:i:2:d:10.1007_s10878-012-9520-9. 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.