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A linear algorithm for secure domination in trees.

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Title: A linear algorithm for secure domination in trees.
Authors: Burger, A.P.1 apburger@sun.ac.za, de Villiers, A.P.1 antondev@sun.ac.za, van Vuuren, J.H.2 vuuren@sun.ac.za
Source: Discrete Applied Mathematics. Jul2014, Vol. 171, p15-27. 13p.
Subjects: Linear statistical models, Dominating set, Set theory, Graph theory, Algorithms
Abstract: Abstract: A subset of the vertex set of a graph is a secure dominating set of if is a dominating set of and if, for each vertex not in , there is a neighbouring vertex of in such that the swap set is again a dominating set of . The secure domination number of , denoted by , is the cardinality of a smallest secure dominating set of . A linear algorithm is proposed in this paper for finding a minimum secure dominating set and hence the value for a tree . The algorithm is based on a strategy of repeatedly pruning away pendent spiders of after having dominated them securely. [Copyright &y& Elsevier]
Copyright of Discrete Applied Mathematics is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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Header DbId: egs
DbLabel: Engineering Source
An: 95502844
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
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  Data: A linear algorithm for secure domination in trees.
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  Data: <searchLink fieldCode="AR" term="%22Burger%2C+A%2EP%2E%22">Burger, A.P.</searchLink><relatesTo>1</relatesTo><i> apburger@sun.ac.za</i><br /><searchLink fieldCode="AR" term="%22de+Villiers%2C+A%2EP%2E%22">de Villiers, A.P.</searchLink><relatesTo>1</relatesTo><i> antondev@sun.ac.za</i><br /><searchLink fieldCode="AR" term="%22van+Vuuren%2C+J%2EH%2E%22">van Vuuren, J.H.</searchLink><relatesTo>2</relatesTo><i> vuuren@sun.ac.za</i>
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  Data: <searchLink fieldCode="JN" term="%22Discrete+Applied+Mathematics%22">Discrete Applied Mathematics</searchLink>. Jul2014, Vol. 171, p15-27. 13p.
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  Data: <searchLink fieldCode="DE" term="%22Linear+statistical+models%22">Linear statistical models</searchLink><br /><searchLink fieldCode="DE" term="%22Dominating+set%22">Dominating set</searchLink><br /><searchLink fieldCode="DE" term="%22Set+theory%22">Set theory</searchLink><br /><searchLink fieldCode="DE" term="%22Graph+theory%22">Graph theory</searchLink><br /><searchLink fieldCode="DE" term="%22Algorithms%22">Algorithms</searchLink>
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  Label: Abstract
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  Data: Abstract: A subset of the vertex set of a graph is a secure dominating set of if is a dominating set of and if, for each vertex not in , there is a neighbouring vertex of in such that the swap set is again a dominating set of . The secure domination number of , denoted by , is the cardinality of a smallest secure dominating set of . A linear algorithm is proposed in this paper for finding a minimum secure dominating set and hence the value for a tree . The algorithm is based on a strategy of repeatedly pruning away pendent spiders of after having dominated them securely. [Copyright &y& Elsevier]
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  Data: <i>Copyright of Discrete Applied Mathematics is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1016/j.dam.2014.02.001
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        Text: English
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        PageCount: 13
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      – SubjectFull: Linear statistical models
        Type: general
      – SubjectFull: Dominating set
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      – SubjectFull: Set theory
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      – SubjectFull: Graph theory
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      – SubjectFull: Algorithms
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      – TitleFull: A linear algorithm for secure domination in trees.
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              Text: Jul2014
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