A1 - Kijewska, Monika
N2 - Domatic partitions of graphs were investigated. The maximum number of classes of a domatic partition of a graph is called the "domatic number" of a graph. The all results in the work can be divided onto five parts. The first concerns the calculating of the domatic partitions of the path, the cycle, the complete bipartite graph and some domatically full graphs. These numbers were defined recursively.
N2 - Moreover, it was given the solutions of recurences using Fibonacci numbers, generating functions. Next it was explored the bounds for the domatic numbers of graph products. It was considered the following graph products: the cartesian product of two graphs, the strong product of two graphs, the join of graphs, the k-corona of two graphs, the contraction of the complete subgraph of a graph into a new vertex and the duplication of a vertex of a graph. It was also characterized the graphs achieving the obtained bounds.
N2 - Relationships between domatic numbers of the bipartite graph and its complement were established. The full characterizations of the k-domatically critical graphs and the k-tuple domatically critical graphs were also given. Several Nordhaus-Gaddum type results for domatic parameters of a graph were presented.
KW - produkty grafów
KW - grafy
KW - podziały domatyczne grafów
KW - liczby domatyczne grafów
T1 - Podziały domatyczne grafów i ich produktów