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Connected domatic number of a graph. (English) Zbl 0625.05042

The connected domatic number of a graph G is the maximum number of subsets in a partition of V(G), each of whose subsets D has the properties that (i) the subgraph induced by it is connected and (ii) for each vertex \(x\in V(G)-D\), there exists a vertex \(y\in D\) adjacent to x. The connected domatic number if well defined only for connected graphs. The author studies a number of properties of the connected domatic number.
Reviewer: G.Chartrand

MSC:

05C99 Graph theory
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References:

[1] COCKAYNE E. J., HEDETNIEMI S. T.: Towards a theory of domination in graphs. Networks 7, 1977, 247-261. · Zbl 0384.05051
[2] COCKAYNE E. J., DAWES R., HEDETNIEMI S. T.: Total domination in graphs. Networks 10, 1980, 211-219. · Zbl 0447.05039
[3] LASKAR R., HEDETNIEMI S. T.: Connected Domination in Graphs. Tech. Report 414, Clemson Univ., Clemson, South Carolina, March 1983. · Zbl 0548.05055
[4] JAEGAR F., PAYAN C.: Relations du type Nordhaus-Gaddum pour le numbre d’absorption d’un graphe simple. C. R. Acad. Sci. Paris, Series A 274, 1972, 728-730. · Zbl 0226.05121
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