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Independent transversal domination in graphs

100%

Hamid I.

Discussiones Mathematicae Graph Theory

2012

tom 32

nr 1

5-17

A set S ⊆ V of vertices in a graph G = (V, E) is called a dominating set if every vertex in V-S is adjacent to a vertex in S. A dominating set which intersects every maximum independent set in G is called an independent transversal dominating set. The minimum cardinality of an independent transversal dominating set is called the independent transversal domination number of G and is denoted by $γ_{it}(G)$. In this paper we begin an investigation of this parameter.

Fractional global domination in graphs

51%

Arumugam S., Karuppasamy K., Hamid I.

Discussiones Mathematicae Graph Theory

2010

tom 30

nr 1

33-44

Let G = (V,E) be a graph. A function g:V → [0,1] is called a global dominating function (GDF) of G, if for every v ∈ V, $g(N[v]) = ∑_{u ∈ N[v]}g(u) ≥ 1$ and $g(\overline{N(v)}) = ∑_{u ∉ N(v)}g(u) ≥ 1$. A GDF g of a graph G is called minimal (MGDF) if for all functions f:V → [0,1] such that f ≤ g and f(v) ≠ g(v) for at least one v ∈ V, f is not a GDF. The fractional global domination number $γ_{fg}(G)$ is defined as follows: $γ_{fg}(G)$ = min{|g|:g is an MGDF of G } where $|g| = ∑_{v ∈ V} g(v)$. In this paper we initiate a study of this parameter.

Ograniczanie wyników

2 Discussiones Mathematicae Graph Theory

2 Hamid I.

1 Arumugam S.

1 Karuppasamy K.

1 2012

1 2010

Wyniki wyszukiwania

Independent transversal domination in graphs

Fractional global domination in graphs