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Minimal connected restrained monophonic sets in graphs

dc.creatorSanthakumaran, A. P.
dc.creatorTitus, P.
dc.creatorGanesamoorthy, K.
dc.date2022-07-26
dc.date.accessioned2022-08-30T15:59:36Z
dc.date.available2022-08-30T15:59:36Z
dc.identifierhttps://www.revistaproyecciones.cl/index.php/proyecciones/article/view/4475
dc.identifier10.22199/issn.0717-6279-4475
dc.identifier.urihttps://revistaschilenas.uchile.cl/handle/2250/207073
dc.descriptionFor a connected graph G = (V,E) of order at least two, a connected restrained monophonic set S of G is a restrained monophonic set such that the subgraph G[S] induced by S is connected. The minimum cardinality of a connected restrained monophonic set of G is the connected restrained monophonic number of G and is denoted by mcr(G). A connected restrained monophonic set S of G is called a minimal connected restrained monophonic set if no proper subset of S is a connected restrained monophonic set of G. The upper connected restrained monophonic number of G, denoted by m+cr(G), is defined as the maximum cardinality of a minimal connected restrained monophonic set of G. We determine bounds for it and certain general properties satisfied by this parameter are studied. It is shown that, for positive integers a, b such that 4≤ a ≤ b , there exists a connected graph G such that  mcr(G) = a and m+cr(G) = b. en-US
dc.formatapplication/pdf
dc.languageeng
dc.publisherUniversidad Católica del Norte.en-US
dc.relationhttps://www.revistaproyecciones.cl/index.php/proyecciones/article/view/4475/4089
dc.rightsCopyright (c) 2022 A. P. Santhakumaran, P. Titus, K. Ganesamoorthyen-US
dc.rightshttps://creativecommons.org/licenses/by/4.0en-US
dc.sourceProyecciones (Antofagasta, On line); Vol. 41 No. 4 (2022); 879-890en-US
dc.sourceProyecciones. Revista de Matemática; Vol. 41 Núm. 4 (2022); 879-890es-ES
dc.source0717-6279
dc.subjectrestrained monophonic seten-US
dc.subjectrestrained monophonic numberen-US
dc.subjectconnected restrained monophonic seten-US
dc.subjectconnected restrained monophonic numberen-US
dc.subjectminimal connected restrained monophonic seten-US
dc.subject05C12en-US
dc.titleMinimal connected restrained monophonic sets in graphsen-US
dc.typeinfo:eu-repo/semantics/article
dc.typeinfo:eu-repo/semantics/publishedVersion
dc.typePeer-reviewed Articleen-US
dc.typetexten-US


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