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On the Total {k}-Domination and Total {k}-Domatic Number of Graphs.
- Source :
-
Bulletin of the Malaysian Mathematical Sciences Society . 2013, Vol. 36 Issue 1, p39-47. 9p. - Publication Year :
- 2013
-
Abstract
- For a positive integer k, a total {k}-dominating function of a graph G without isolated vertices is a function f from the vertex set V(G) to the set {0,1,2, . . . ,k} such that for any vertex v ∊ V(G), the condition Σu∊N(v) f (u) ≥ k is fulfilled, where N(v) is the open neighborhood of v. The weight of a total {k}-dominating function f is the value ω(f) = Σv∊V f (v). The total {k}-domination number, denoted by γt{k} (G), is the minimum weight of a total {k}-dominating function on G. A set {f1, f2, . . . , fd} of total {k}-dominating functions on G with the property that Σdi =1 fi(v) ≤ k for each v ∊ V(G), is called a total {k}-dominating family (of functions) on G. The maximum number of functions in a total {k}-dominating family on G is the total {k}-domatic number of G, denoted by dt{k} (G). Note that dt{1} (G) is the classic total domatic number dt(G). In this paper, we present bounds for the total {k}-domination number and total {k}-domatic number. In addition, we determine the total {k}-domatic number of cylinders and we give a Nordhaus-Gaddum type result. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 01266705
- Volume :
- 36
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Bulletin of the Malaysian Mathematical Sciences Society
- Publication Type :
- Academic Journal
- Accession number :
- 109134514