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Displaying similar documents to “On signed majority 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....

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 distance- k -domination in graphs

Hua Ming Xing, Liang Sun, Xue-Gang Chen (2006)

Czechoslovak Mathematical Journal

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The signed distance- k -domination number of a graph is a certain variant of the signed domination number. If v is a vertex of a graph G , the open k -neighborhood of v , denoted by N k ( v ) , is the set N k ( v ) = { u u v and d ( u , v ) k } . N k [ v ] = N k ( v ) { v } is the closed k -neighborhood of v . A function f V { - 1 , 1 } is a signed distance- k -dominating function of G , if for every vertex v V , f ( N k [ v ] ) = u N k [ v ] f ( u ) 1 . The signed distance- k -domination number, denoted by γ k , s ( G ) , is the minimum weight of a signed distance- k -dominating function on G . The values of γ 2 , s ( G ) are found for graphs...