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The upper open monophonic number of a graph

dc.creatorSanthakumaran, A. P.
dc.creatorMahendran, M.
dc.date2017-03-23
dc.date.accessioned2019-11-14T11:59:13Z
dc.date.available2019-11-14T11:59:13Z
dc.identifierhttps://www.revistaproyecciones.cl/article/view/1270
dc.identifier10.4067/S0716-09172014000400003
dc.identifier.urihttps://revistaschilenas.uchile.cl/handle/2250/113061
dc.descriptionFor a connected graph G of order n,a subset S of vertices of G is a monophonic set of G if each vertex v in G lies on a x-y monophonic path for some elements x and y in S. The minimum cardinality of a monophonic set of G is defined as the monophonic number of G, denoted by m(G). A monophonic set of cardinality m(G) is called a m-set of G.A set S of vertices of a connected graph G is an open monophonic set of G if for each vertex v in G ,either v is an extreme vertex of G and v G S,or v is an internal vertex of a x-y mono-phonic path for some x,y G S. An open monophonic set of minimum cardinality is a minimum open monophonic set and this cardinality is the open monophonic number, om(G). An open monophonic set S of vertices in a connected graph G is a minimal open monophonic .set if no proper subset of S is an open monophonic set of G.The upper open monophonic number om+ (G) is the maximum cardinality of a minimal open monophonic set of G. The upper open monophonic numbers of certain standard graphs are determined. It is proved that for a graph G of order n, om(G) = n if and only if om+(G)= n. Graphs G with om(G) = 2 are characterized. If a graph G has a minimal open monophonic set S of cardinality 3, then S is also a minimum open monophonic set of G and om(G) = 3. For any two positive integers a and b with 4 < a < b, there exists a connected graph G with om(G) = a and om+(G) = b.es-ES
dc.formatapplication/pdf
dc.languagespa
dc.publisherUniversidad Católica del Norte.es-ES
dc.relationhttps://www.revistaproyecciones.cl/article/view/1270/982
dc.rightsDerechos de autor 2014 Proyecciones. Journal of Mathematicses-ES
dc.sourceProyecciones. Journal of Mathematics; Vol 33 No 4 (2014); 389-403en-US
dc.sourceProyecciones. Revista de Matemática; Vol. 33 Núm. 4 (2014); 389-403es-ES
dc.source0717-6279
dc.source0716-0917
dc.subjectDistancees-ES
dc.subjectgeodesices-ES
dc.subjectgeodetic numberes-ES
dc.subjectopen geodetic numberes-ES
dc.subjectmonophonic numberes-ES
dc.subjectopen monophonic numberes-ES
dc.subjectupper open monophonic numberes-ES
dc.subjectdistanciaes-ES
dc.subjectgeodesiaes-ES
dc.subjectnúmero geodésicoes-ES
dc.subjectnúmero geodésico abiertoes-ES
dc.subjectnúmero monofónicoes-ES
dc.subjectnúmero monofónico abierto.es-ES
dc.titleThe upper open monophonic number of a graphes-ES
dc.typeinfo:eu-repo/semantics/article
dc.typeinfo:eu-repo/semantics/publishedVersion
dc.typeArtículo revisado por pareses-ES


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