| dc.creator | Santhakumaran, A. P. | |
| dc.creator | Venkata Raghu, T. | |
| dc.date | 2018-06-06 | |
| dc.date.accessioned | 2019-06-28T17:06:29Z | |
| dc.date.available | 2019-06-28T17:06:29Z | |
| dc.identifier | http://www.revistaproyecciones.cl/article/view/2929 | |
| dc.identifier.uri | https://revistaschilenas.uchile.cl/handle/2250/101121 | |
| dc.description | A set S of a connected graph G of order n is called a double monophonic set of G if for every pair of vertices x, y in G there exist vertices u, v in S such that x, y lie on a u − v monophonic path. The double monophonic number dm(G) of G is the minimum cardinality of a double monophonic set. A double monophonic set S in a connected graph G is called a minimal double monophonic set if no proper subset of S is a double monophonic set of G. The upper double monophonic number of G is the maximum cardinality of a minimal double monophonic set of G, and is denoted by dm⁺(G). Some general properties satisfied by upper double monophonic sets are discussed. It is proved that for a connected graph G of order n, dm(G) = n if and only if dm⁺(G) = n. It is also proved that dm(G) = n − 1 if and only if dm⁺ (G) = n − 1 for a non-complete graph G of order n with a full degree vertex. For any positive integers 2 ≤ a ≤ b, there exists a connected graph G with dm(G) = a and dm⁺(G) = b. | en-US |
| dc.format | application/pdf | |
| dc.language | eng | |
| dc.publisher | Universidad Católica del Norte. | es-ES |
| dc.relation | http://www.revistaproyecciones.cl/article/view/2929/2766 | |
| dc.rights | Derechos de autor 2018 Proyecciones. Journal of Mathematics | es-ES |
| dc.rights | https://creativecommons.org/licenses/by-nc/4.0/ | es-ES |
| dc.source | Proyecciones. Journal of Mathematics; Vol 37 No 2 (2018); 295-304 | en-US |
| dc.source | Proyecciones. Revista de Matemática; Vol. 37 Núm. 2 (2018); 295-304 | es-ES |
| dc.source | 0717-6279 | |
| dc.source | 0716-0917 | |
| dc.title | Upper double monophonic number of a graph. | en-US |
| dc.type | info:eu-repo/semantics/article | |
| dc.type | info:eu-repo/semantics/publishedVersion | |
| dc.type | Artículo revisado por pares | es-ES |
