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Complementarily domatic number of a graph. (English) Zbl 0641.05045

Let D be a subset of the vertex set V(G) of a graph G. The set D is called complementarily domination if for each vertex \(x\in V(G)-D\) there exist vertices \(y\in D\), \(z\in D\) such that y is adjacent and z is non- adjacent to x in G. A complementarily domatic partition of G is a partition of V(G), all of whose classes are complementarily dominating sets in G. The maximum number of classes of a complementarily domatic partition of G is called the complementarily domatic number of G and denoted by \(d_{cp}(G)\). Thus \(d_{cp}(G)\) is a variant of the domatic number of a graph introduced by E. J. Cockayne and S. T. Hedetiemi [Networks 7, 247-261 (1977; Zbl 0384.05051)]. Here bounds for \(d_{cp}(G)\) are given for graphs G in various classes.
Reviewer: R.C.Entringer

MSC:

05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.)

Citations:

Zbl 0384.05051
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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, 211-215. · Zbl 0447.05039
[3] LASKAR R., HEDETNIEMI S. T.: Connected domination in graphs. Report 414, Clemson Univ., Clemson, South Carolina, March 1983. · Zbl 0548.05055
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