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Total domatic number of cacti. (English) Zbl 0654.05059
A total domatic coloring of a graph G is a vertex coloring of G with the property that each vertex of G is adjacent to vertices of all colors. The maximum number of colors of a total domatic coloring is called the total domatic number of G. This invariant was introduced by E. J. Cockayne, R. M. Dawes and S. T. Hedetniemi [Networks 10, 211-219 (1980; Zbl 0447.05039)]. The author studies the total domatic number of cacti.
Reviewer: R.C.Entringer

MSC:
05C99 Graph theory
05C15 Coloring of graphs and hypergraphs
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References:
[1] COCKAYNE E. J., DAWES R. M., HEDETNIEMI S. T.: Total domination in graphs. Networks 10, 1980, 211-219. · Zbl 0447.05039
[2] ZELINKA B.: Total domatic number of a graph. Časop. p\?st. mat. · Zbl 0743.05033
[3] ZELINKA B.: Domatic number and linear arboricity of cacti. Math. Slovaca 36, 1986, 49-54. · Zbl 0583.05050
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