Displaying similar documents to “Minus total domination in graphs”

On total restrained domination in graphs

De-xiang Ma, Xue-Gang Chen, Liang Sun (2005)

Czechoslovak Mathematical Journal

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In this paper we initiate the study of total restrained domination in graphs. 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 . First, some exact values and sharp bounds for γ r t ( G ) are given in Section 2....

A bound on the k -domination number of a graph

Lutz Volkmann (2010)

Czechoslovak Mathematical Journal

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Let G be a graph with vertex set V ( G ) , and let k ≥ 1 be an integer. A subset D ⊆ V ( G ) is called a if every vertex v ∈ V ( G ) - D has at least k neighbors in D . The k -domination number γ k ( G ) of G is the minimum cardinality of a k -dominating set in G . If G is a graph with minimum degree δ ( G ) ≥ k + 1 , then we prove that γ k + 1 ( G ) ≤ | V ( G ) | + γ k ( G ) 2 . In addition, we present a characterization of a special class of graphs attaining equality in this inequality.

On signed majority total domination in graphs

Hua Ming Xing, Liang Sun, Xue-Gang Chen (2005)

Czechoslovak Mathematical Journal

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We initiate the study of signed majority total domination in graphs. Let G = ( V , E ) be a simple graph. For any real valued function f V → ℝ and S ⊆ V , let f ( S ) = ∑ v ∈ S f ( v ) . A signed majority total dominating function is a function f V → { - 1 , 1 } such that f ( N ( v ) ) ≥ 1 for at least a half of the vertices v ∈ V . The signed majority total domination number of a graph G is γ m a j t ( G ) = min { f ( V ) ∣ f is a signed majority total dominating function on G } . We research some properties of the signed majority total domination number of a graph G and obtain a few lower bounds of γ m a j t ( G ) . ...

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...

Vertex-disjoint stars in graphs

Katsuhiro Ota (2001)

Discussiones Mathematicae Graph Theory

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In this paper, we give a sufficient condition for a graph to contain vertex-disjoint stars of a given size. It is proved that if the minimum degree of the graph is at least k+t-1 and the order is at least (t+1)k + O(t²), then the graph contains k vertex-disjoint copies of a star K 1 , t . The condition on the minimum degree is sharp, and there is an example showing that the term O(t²) for the number of uncovered vertices is necessary in a sense.

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...