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Security, (F,I)-security, and Ultra-security in Graphs


Metadata FieldValueLanguage
dc.contributor.advisorJohnson, Peter
dc.contributor.advisorRodger, Chris
dc.contributor.advisorHoffman, Dean
dc.contributor.authorPetrie, Caleb
dc.date.accessioned2012-08-02T15:25:08Z
dc.date.available2012-08-02T15:25:08Z
dc.date.issued2012-08-02
dc.identifier.urihttp://hdl.handle.net/10415/3306
dc.description.abstractLet G=(V,E) be a graph and S a subset of V. The notion of security in graphs was first presented by Brigham et al [3]. A set S is secure if every attack on S is defendable. The cardinality of a smallest secure set of G is the security number of G. We give several new definitions of security. We show that some of these new definitions are equivalent to the definition given by Brigham et al, while others are not. In these new situations, we find necessary and sufficient conditions for security. Various Hall-type theorems are used in these proofs. We also define analogues of the security number and find them for various classes of graphs.en_US
dc.rightsEMBARGO_GLOBALen_US
dc.subjectMathematics and Statisticsen_US
dc.titleSecurity, (F,I)-security, and Ultra-security in Graphsen_US
dc.typedissertationen_US
dc.embargo.lengthMONTHS_WITHHELD:12en_US
dc.embargo.statusEMBARGOEDen_US
dc.embargo.enddate2013-08-02en_US

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