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

Similarity:

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

Similarity:

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

Similarity:

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...