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The total {k}-domatic number of wheels and complete graphs
- Source :
- Journal of Combinatorial Optimization. 24:162-175
- Publication Year :
- 2010
- Publisher :
- Springer Science and Business Media LLC, 2010.
-
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.
Details
- ISSN :
- 15732886 and 13826905
- Volume :
- 24
- Database :
- OpenAIRE
- Journal :
- Journal of Combinatorial Optimization
- Accession number :
- edsair.doi...........1604b4d4aa83565d8ad59e89aeb8f7ca