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Domination in cubes. (English) Zbl 0753.05056
Summary: The graph of the \(n\)-dimensional cube is the graph whose vertex set is the set of all \(n\)-dimensional Boolean vectors and in which two vertices are adjacent if and only if they differ in exactly one coordinate. In the paper the \(k\)-domatic number and the edge-domatic number of these graphs are studied.

MSC:
05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.)
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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 · doi:10.1002/net.3230070305
[2] ZELINKA B.: Edge-domatic number of a graph. Czech. Math. J., 33, 1983, 107-110. · Zbl 0537.05049 · eudml:13366
[3] ZELINKA B.: On k-domatic numbers of graphs. Czech. Math. J., 33, 1983, 309-311. · Zbl 0537.05050 · eudml:13384
[4] ZELINKA B.: Domatic number of cube graphs. Math. Slvovaca, 32, 1982, 117-119. · Zbl 0487.05057 · eudml:31883
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