| dc.creator | Santhakumaran, A. P. | es |
| dc.creator | Mahendran, M. | es |
| dc.date | 2017-03-23 | |
| dc.date.accessioned | 2025-10-06T15:04:55Z | |
| dc.date.available | 2025-10-06T15:04:55Z | |
| dc.identifier | https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/1270 | |
| dc.identifier | 10.4067/S0716-09172014000400003 | |
| dc.identifier.uri | https://revistaschilenas.uchile.cl/handle/2250/255440 | |
| dc.description | For 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 |
| dc.format | application/pdf | |
| dc.language | spa | |
| dc.publisher | Universidad Católica del Norte. | en |
| dc.relation | https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/1270/982 | |
| dc.rights | Copyright (c) 2014 Proyecciones. Journal of Mathematics | en |
| dc.rights | https://creativecommons.org/licenses/by/4.0 | en |
| dc.source | Proyecciones (Antofagasta); Vol. 33 No. 4 (2014); 389-403 | en |
| dc.source | Proyecciones. Revista de Matemática; Vol. 33 Núm. 4 (2014); 389-403 | es |
| dc.source | 0717-6279 | |
| dc.source | 10.22199/issn.0717-6279-2014 | |
| dc.title | The upper open monophonic number of a graph | es |
| dc.type | info:eu-repo/semantics/article | |
| dc.type | info:eu-repo/semantics/publishedVersion | |
