IDEAS home Printed from https://ideas.repec.org/a/spr/cejnor/v23y2015i3p659-673.html
   My bibliography  Save this article

$$L(3,2,1)$$ L ( 3 , 2 , 1 ) -labeling of triangular and toroidal grids

Author

Listed:
  • Zehui Shao
  • Aleksander Vesel

Abstract

The $$L(3,2,1)$$ L ( 3 , 2 , 1 ) -labeling of a graph is an abstraction of assigning integer frequencies to radio transceivers such that (1) transceivers that are one unit of distance apart receive frequencies that differ by at least three, (2) transceivers that are two units of distance apart receive frequencies that differ by at least two, and (3) transceivers that are three units of distance apart receive frequencies that differ by at least one. The least span of frequencies in such a labeling is referred to as the $$\uplambda _{3,2,1}$$ λ 3 , 2 , 1 -number of the graph. In this paper, we determine the $$\uplambda _{3,2,1}$$ λ 3 , 2 , 1 -number for toroidal grids $$T_{n,m}, m \le 6$$ T n , m , m ≤ 6 and the $$\uplambda _{3,2,1}$$ λ 3 , 2 , 1 -number for the triangular grid. The last result proves the conjecture from Calamoneri (Inf Process Lett 113:361–364, 2013 ). Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Zehui Shao & Aleksander Vesel, 2015. "$$L(3,2,1)$$ L ( 3 , 2 , 1 ) -labeling of triangular and toroidal grids," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 23(3), pages 659-673, September.
    • Handle: RePEc:spr:cejnor:v:23:y:2015:i:3:p:659-673
    DOI: 10.1007/s10100-014-0365-4
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10100-014-0365-4
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10100-014-0365-4?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. Dupont, Audrey & Linhares, Andréa Carneiro & Artigues, Christian & Feillet, Dominique & Michelon, Philippe & Vasquez, Michel, 2009. "The dynamic frequency assignment problem," European Journal of Operational Research, Elsevier, vol. 195(1), pages 75-88, May.
    2. Jelena Govorčin & Nebojša Gvozdenović & Janez Povh, 2013. "New heuristics for the vertex coloring problem based on semidefinite programming," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 21(1), pages 13-25, June.
    3. Tiziana Calamoneri & Emanuele Fusco & Richard Tan & Paola Vocca, 2009. "L(h, 1, 1)-labeling of outerplanar graphs," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 69(2), pages 307-321, May.
    4. Smith, D. H. & Hurley, S. & Thiel, S. U., 1998. "Improving heuristics for the frequency assignment problem," European Journal of Operational Research, Elsevier, vol. 107(1), pages 76-86, May.
    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. Montemanni, R. & Smith, D. H. & Allen, S. M., 2004. "An improved algorithm to determine lower bounds for the fixed spectrum frequency assignment problem," European Journal of Operational Research, Elsevier, vol. 156(3), pages 736-751, August.
    2. Karen Aardal & Stan Hoesel & Arie Koster & Carlo Mannino & Antonio Sassano, 2007. "Models and solution techniques for frequency assignment problems," Annals of Operations Research, Springer, vol. 153(1), pages 79-129, September.
    3. Bradley Hardy & Rhyd Lewis & Jonathan Thompson, 2018. "Tackling the edge dynamic graph colouring problem with and without future adjacency information," Journal of Heuristics, Springer, vol. 24(3), pages 321-343, June.
    4. Zehui Shao & Aleksander Vesel & Jin Xu, 2017. "Frequency assignment problem in networks with limited spectrum," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 25(3), pages 699-723, September.
    5. Iztok Fister & Marjan Mernik & Bogdan Filipič, 2013. "Graph 3-coloring with a hybrid self-adaptive evolutionary algorithm," Computational Optimization and Applications, Springer, vol. 54(3), pages 741-770, April.
    6. Andrej Kastrin & Janez Povh & Lidija Zadnik Stirn & Janez Žerovnik, 2021. "Methodologies and applications for resilient global development from the aspect of SDI-SOR special issues of CJOR," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 29(3), pages 773-790, September.
    7. Lü, Zhipeng & Hao, Jin-Kao, 2010. "A memetic algorithm for graph coloring," European Journal of Operational Research, Elsevier, vol. 203(1), pages 241-250, May.
    8. Tibor Csendes & Lidija Zadnik Stirn & Janez Žerovnik, 2013. "Editorial," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 21(1), pages 1-2, June.

    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:cejnor:v:23:y:2015:i:3:p:659-673. 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.