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Partitioning a graph into a dominating set, a total dominating set, and something else

100%

Henning M., Löwenstein C., Rautenbach D.

Discussiones Mathematicae Graph Theory

2010

tom 30

nr 4

563-574

A recent result of Henning and Southey (A note on graphs with disjoint dominating and total dominating set, Ars Comb. 89 (2008), 159-162) implies that every connected graph of minimum degree at least three has a dominating set D and a total dominating set T which are disjoint. We show that the Petersen graph is the only such graph for which D∪T necessarily contains all vertices of the graph.

The B-Domatic Number of a Graph

86%

Favaron O.

Discussiones Mathematicae Graph Theory

2013

tom 33

nr 4

747-757

Besides the classical chromatic and achromatic numbers of a graph related to minimum or minimal vertex partitions into independent sets, the b-chromatic number was introduced in 1998 thanks to an alternative definition of the minimality of such partitions. When independent sets are replaced by dominating sets, the parameters corresponding to the chromatic and achromatic numbers are the domatic and adomatic numbers d(G) and ad(G). We introduce the b-domatic number bd(G) as the counterpart of the b-chromatic number by giving an alternative definition of the maximality of a partition into dominating sets. We initiate the study of bd(G) by giving some properties and examples.

Ograniczanie wyników

2 Discussiones Mathematicae Graph Theory

1 Favaron O.

1 Henning M.

1 Löwenstein C.

1 Rautenbach D.

1 2013

1 2010

Wyniki wyszukiwania

Partitioning a graph into a dominating set, a total dominating set, and something else

The B-Domatic Number of a Graph