IDEAS home Printed from https://ideas.repec.org/a/spr/jcomop/v24y2012i3d10.1007_s10878-010-9374-y.html
   My bibliography  Save this article

The total {k}-domatic number of wheels and complete graphs

Author

Listed:
  • Jing Chen

    (University of Science and Technology of China)

  • Xinmin Hou

    (University of Science and Technology of China)

  • Ning Li

    (University of Science and Technology of China)

Abstract

Let k be a positive integer and let G be a graph with vertex set V(G). The total {k}-dominating function (T{k}DF) of a graph G is a function f from V(G) to the set {0,1,2,…,k}, such that for each vertex v∈V(G), the sum of the values of all its neighbors assigned by f is at least k. A set {f 1,f 2,…,f d } of pairwise different T{k}DFs of G with the property that $\sum_{i=1}^{d}f_{i}(v)\leq k$ for each v∈V(G), is called a total {k}-dominating family (T{k}D family) of G. The total {k}-domatic number of a graph G, denoted by $d_{t}^{\{k\}}(G)$ , is the maximum number of functions in a T{k}D family. In this paper, we determine the exact values of the total {k}-domatic numbers of wheels and complete graphs, which answers an open problem of Sheikholeslami and Volkmann (J. Comb. Optim., 2010) and completes a result in the same paper.

Suggested Citation

  • Jing Chen & Xinmin Hou & Ning Li, 2012. "The total {k}-domatic number of wheels and complete graphs," Journal of Combinatorial Optimization, Springer, vol. 24(3), pages 162-175, October.
    • Handle: RePEc:spr:jcomop:v:24:y:2012:i:3:d:10.1007_s10878-010-9374-y
    DOI: 10.1007/s10878-010-9374-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10878-010-9374-y
    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/s10878-010-9374-y?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. Jia-Xiong Dan & Zhi-Bo Zhu & Xin-Kui Yang & Ru-Yi Li & Wei-Jie Zhao & Xiang-Jun Li, 2022. "The signed edge-domatic number of nearly cubic graphs," Journal of Combinatorial Optimization, Springer, vol. 44(1), pages 435-445, August.

    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:24:y:2012:i:3:d:10.1007_s10878-010-9374-y. 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.