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Displaying similar documents to “On total restrained domination in graphs”

Minus total domination in graphs

Hua Ming Xing, Hai-Long Liu (2009)

Czechoslovak Mathematical Journal

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A three-valued function f V { - 1 , 0 , 1 } defined on the vertices of a graph G = ( V , E ) is a minus total dominating function (MTDF) if the sum of its function values over any open neighborhood is at least one. That is, for every v V , f ( N ( v ) ) 1 , where N ( v ) consists of every vertex adjacent to v . The weight of an MTDF is f ( V ) = f ( v ) , over all vertices v V . The minus total domination number of a graph G , denoted γ t - ( G ) , equals the minimum weight of an MTDF of G . In this paper, we discuss some properties of minus total domination on a graph...

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 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 ) . ...

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.