Wyniki wyszukiwania

Sortuj według:

Ogranicz wyniki do:

Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik

Trees with equal total domination and total restrained domination numbers

100%

Chen X.-G., Shiu W., Chen H.-Y.

Discussiones Mathematicae Graph Theory

2008

tom 28

nr 1

59-66

For a graph G = (V,E), a set S ⊆ V(G) is a total dominating set if it is dominating and both ⟨S⟩ has no isolated vertices. The cardinality of a minimum total dominating set in G is the total domination number. A set S ⊆ V(G) is a total restrained dominating set if it is total dominating and ⟨V(G)-S⟩ has no isolated vertices. The cardinality of a minimum total restrained dominating set in G is the total restrained domination number. We characterize all trees for which total domination and total restrained domination numbers are the same.

On the total restrained domination number of direct products of graphs

100%

Shiu W., Chen H.-Y., Chen X.-G., Sun P.

Discussiones Mathematicae Graph Theory

2012

tom 32

nr 4

629-641

Let G = (V,E) be a graph. A total restrained dominating set is a set S ⊆ V where every vertex in V∖S is adjacent to a vertex in S as well as to another vertex in V∖S, and every vertex in S is adjacent to another vertex in S. The total restrained domination number of G, denoted by $γ_r^t(G)$, is the smallest cardinality of a total restrained dominating set of G. We determine lower and upper bounds on the total restrained domination number of the direct product of two graphs. Also, we show that these bounds are sharp by presenting some infinite families of graphs that attain these bounds.

Ograniczanie wyników

2 Discussiones Mathematicae Graph Theory

2 Chen H.-Y.

2 Chen X.-G.

2 Shiu W.

1 Sun P.

1 2012

1 2008

Wyniki wyszukiwania

Trees with equal total domination and total restrained domination numbers

On the total restrained domination number of direct products of graphs