Gated independence in graphs

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dc.authorscopusid35611132200en_US
dc.authorscopusid56462806000en_US
dc.authorscopusid57208254403en_US
dc.contributor.authorCivan, Yusuf
dc.contributor.authorDeniz, Zakir
dc.contributor.authorYetim, Mehmet Akif
dc.date.accessioned2024-08-23T16:04:50Z
dc.date.available2024-08-23T16:04:50Z
dc.date.issued2024en_US
dc.departmentDüzce Üniversitesien_US
dc.description.abstractIf G = ( V , E ) is a (finite and simple) graph, we call an independent set X a gated independent set in G if for each x is an element of X , there exists a neighbor y of x such that ( X \ { x } ) boolean OR{ y } is an independent set in G . We define the gated independence number gi( G ) of G to be the maximum cardinality of a gated independent set in G . We demonstrate that the gated independence number is closely related to both matching and domination parameters of graphs. We prove that the inequalities im( G ) gi( G ) m ur ( G ) hold for every graph G , where im( G ) and m ur ( G ) denote the induced and uniquely restricted matching numbers of G . On the other hand, we show that gamma i ( G ) gi( G ) and gamma p r ( G ) 2 gi( G ) for every graph G without any isolated vertex, where gamma i ( G ) and gamma p r ( G ) denote the independence and paired domination numbers. Furthermore, we provide bounds on the gated independence number involving the order, size and maximum degree. In particular, we prove that gi( G ) 5 n for every n -vertex subcubic graph G without any isolated vertex or any component isomorphic to K 3 , 3 , and gi( B ) 3 n 8 for every n -vertex connected cubic bipartite graph B . (c) 2024 Elsevier B.V. All rights reserved.en_US
dc.identifier.doi10.1016/j.dam.2024.04.011
dc.identifier.endpage138en_US
dc.identifier.issn0166-218X
dc.identifier.issn1872-6771
dc.identifier.scopus2-s2.0-85192100804en_US
dc.identifier.scopusqualityQ2en_US
dc.identifier.startpage121en_US
dc.identifier.urihttps://doi.org/10.1016/j.dam.2024.04.011
dc.identifier.urihttps://hdl.handle.net/20.500.12684/14387
dc.identifier.volume353en_US
dc.identifier.wosWOS:001238806400001en_US
dc.identifier.wosqualityN/Aen_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.language.isoenen_US
dc.publisherElsevieren_US
dc.relation.ispartofDiscrete Applied Mathematicsen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subjectInduced matchingen_US
dc.subjectUniquely restricted matchingen_US
dc.subjectGated independent seten_US
dc.subjectDominationen_US
dc.subjectLower Boundsen_US
dc.titleGated independence in graphsen_US
dc.typeArticleen_US

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