Displaying similar documents to “Inequalities involving independence domination, f -domination, connected and total f -domination numbers”

On domination number of 4-regular graphs

Hailong Liu, Liang Sun (2004)

Czechoslovak Mathematical Journal

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Let G be a simple graph. A subset S ⊆ V is a dominating set of G , if for any vertex v ∈ V - S there exists a vertex u ∈ S such that u v ∈ E ( G ) . The domination number, denoted by γ ( G ) , is the minimum cardinality of a dominating set. In this paper we prove that if G is a 4-regular graph with order n , then γ ( G ) ≤ 4 11 n .

A note on the domination number of a graph and its complement

Dănuţ Marcu (2001)

Mathematica Bohemica

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If G is a simple graph of size n without isolated vertices and G ¯ is its complement, we show that the domination numbers of G and G ¯ satisfy γ ( G ) + γ ( G ¯ ) ≤ n - δ + 2 if γ ( G ) > 3 , δ + 3 if γ ( G ¯ ) > 3 , where δ is the minimum degree of vertices in G .

Bounds concerning the alliance number

Grady Bullington, Linda Eroh, Steven J. Winters (2009)

Mathematica Bohemica

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P. Kristiansen, S. M. Hedetniemi, and S. T. Hedetniemi, in Alliances in graphs, J. Combin. Math. Combin. Comput. 48 (2004), 157–177, and T. W. Haynes, S. T. Hedetniemi, and M. A. Henning, in Global defensive alliances in graphs, Electron. J. Combin. 10 (2003), introduced the defensive alliance number a ( G ) , strong defensive alliance number a ^ ( G ) , and global defensive alliance number γ a ( G ) . In this paper, we consider relationships between these parameters and the domination number γ ( G ) . For any positive...

Independent transversal domination in graphs

Ismail Sahul Hamid (2012)

Discussiones Mathematicae Graph Theory

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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 i t ( G ) . In this paper we begin an investigation of this parameter.