Displaying similar documents to “A bound on the k -domination number of a graph”

The cobondage number of a graph

V.R. Kulli, B. Janakiram (1996)

Discussiones Mathematicae Graph Theory

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A set D of vertices in a graph G = (V,E) is a dominating set of G if every vertex in V-D is adjacent to some vertex in D. The domination number γ(G) of G is the minimum cardinality of a dominating set. We define the cobondage number b c ( G ) of G to be the minimum cardinality among the sets of edges X ⊆ P₂(V) - E, where P₂(V) = X ⊆ V:|X| = 2 such that γ(G+X) < γ(G). In this paper, the exact values of bc(G) for some standard graphs are found and some bounds are obtained. Also, a Nordhaus-Gaddum...

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 .

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...

Homogeneously embedding stratified graphs in stratified graphs

Gary Chartrand, Donald W. Vanderjagt, Ping Zhang (2005)

Mathematica Bohemica

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A 2-stratified graph G is a graph whose vertex set has been partitioned into two subsets, called the strata or color classes of G . Two 2 -stratified graphs G and H are isomorphic if there exists a color-preserving isomorphism φ from G to H . A 2 -stratified graph G is said to be homogeneously embedded in a 2 -stratified graph H if for every vertex x of G and every vertex y of H , where x and y are colored the same, there exists an induced 2 -stratified subgraph H ' of H containing y and a color-preserving...