TITLE

# On the Total {k}-Domination and Total {k}-Domatic Number of Graphs

AUTHOR(S)
ARAM, H.; SHEIKHOLESLAMI, S. M.; VOLKMANN, L.
PUB. DATE
January 2013
SOURCE
Asian Academy of Management Journal of Accounting & Finance;2013, Vol. 9 Issue 1, p39
SOURCE TYPE
DOC. TYPE
Article
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 Ïµ V(G), the condition Î£uÏµN(v) f (u) â©¾ k is fulfilled, where N(v) is the open neighborhood of v. The weight of a total {k}-dominating function f is the value Ï‰(f) = Î£vÏµV f(v). The total {k}-domination number, denoted by Î³{k}t (G), is the minimum weight of a total {k}-dominating function on G. A set {f1, f2,â€¦,fd} of total {k}-dominating functions on G with the property that Î£di=1 fi(v) â©½ k for each v Ïµ 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 d{k}t (G). Note that d{1}t (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.
ACCESSION #
88053625

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