Paired bondage in trees

Raczek, Joanna

doi:10.1016/j.disc.2007.10.010

Cited by 13 publications

(5 citation statements)

References 7 publications

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“…However the first result on bondage numbers is obtained by Bauer et al [1]. There are many research articles on the bondage number for undirected graphs and digraphs (see, for example [1]∼ [2], [5] ∼ [17], [19,20], [22] ∼ [28], [31]). In particular, Hu and Xu [13] have showed that the problem determining bondage number for general graphs is NP-hard.…”

Section: A Nonempty Subset B ⊆ E(g) Is Said a Bondage Set Of G If γ(Gmentioning

confidence: 98%

Bondage number of mesh networks

2012

Front. Math. China

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Section: A Nonempty Subset B ⊆ E(g) Is Said a Bondage Set Of G If γ(Gmentioning

confidence: 98%

Bondage number of mesh networks

2012

Front. Math. China

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“…A constructive characterization of trees with ( ) = 2 is given by Hartnell and Rall in [12]. Raczek [73] provided a constructive characterization of trees with ( ) = 0. In order to state the characterization, we define a labeling and three simple operations on a tree .…”

Section: Corollary 122 the Bondage Number And The Paired Bondage Nummentioning

confidence: 99%

“…Raczek [73] obtained the following characterization of all trees with ( ) = 0. The concept of restrained domination was introduced by Telle and Proskurowski [74] in 1997, albeit indirectly, as a vertex partitioning problem.…”

Section: Corollary 122 the Bondage Number And The Paired Bondage Nummentioning

confidence: 99%

On Bondage Numbers of Graphs: A Survey with Some Comments

2013

International Journal of Combinatorics

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The domination number of a graph is the smallest number of vertices which dominate all remaining vertices by edges of . The bondage number of a nonempty graph is the smallest number of edges whose removal from results in a graph with domination number greater than the domination number of . The concept of the bondage number was formally introduced by Fink et al. in 1990. Since then, this topic has received considerable research attention and made some progress, variations, and generalizations. This paper gives a survey on the bondage number, including known results, conjectures, problems, and some comments, also selectively summarizes other types of bondage numbers.

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“…The concept of bondage in graphs was introduced by Bauer, Harary, Nieminen and Suffel in [1], and has been further studied for example in [4,6,8,10,11,13,18,21]. This concept has been considered for several domination parameters, and for a survey of results and recent developments on bondage we refer the reader to [22].…”

Section: Introductionmentioning

confidence: 99%

NP-hardness of multiple bondage in graphs

Rad

2015

Journal of Complexity

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a b s t r a c tLet p ≥ 2 be a positive integer. The p-bondage number of a graph G is the minimum number of edges whose removal from G results in a graph with larger p-domination number. The p-total bondage number of a graph G with no isolated vertex is the minimum number of non-pendant edges whose removal from G results in a graph with larger p-total domination number. The nonisolating p-bondage number of G is the minimum number of nonpendant edges whose removal from G results in a graph with larger p-domination number. In this paper we show that the decision problems for these multiple bondage problems are NP-hard.

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Paired bondage in trees

Abstract: Let G = (V, E) be a graph with δ(G) ≥ 1. A set D ⊆ V is a paired dominating set if D is dominating, and the induced subgraph D contains a perfect matching. The paired domination number of G, denoted by γ p (G), is the minimum cardinality of a paired dominating set of G.

Cited by 13 publications

References 7 publications

Bondage number of mesh networks

Bondage number of mesh networks

On Bondage Numbers of Graphs: A Survey with Some Comments

NP-hardness of multiple bondage in graphs

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