Total domatic number and degrees of vertices of a graph. (English) Zbl 0688.05066

The total domatic number of a graph G, denoted by \(d_ t(G)\) is defined. A result concerning a lower bound for \(d_ t(G)\), in terms of \(\delta\) (G) and the number of vertices of G, is proved.
If G is a finite graph with n (\(\geq 9)\) vertices and \(\delta (G)=n-3\), it is shown that \(d_ t(G)=[n/2].\) It is further shown that \(d_ t(G)<[n/2]\) if \(3\leq n\leq 8\).
Reviewer: I.H.Nagaraja Rao


05C99 Graph theory
Full Text: EuDML


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