| dc.creator | Santhakumaran, A. P. | |
| dc.creator | Titus, P. | |
| dc.creator | Ganesamoorthy, K. | |
| dc.date | 2018-09-24 | |
| dc.date.accessioned | 2019-11-14T12:01:15Z | |
| dc.date.available | 2019-11-14T12:01:15Z | |
| dc.identifier | https://www.revistaproyecciones.cl/article/view/3161 | |
| dc.identifier.uri | https://revistaschilenas.uchile.cl/handle/2250/113647 | |
| dc.description | For a connected graph G = (V, E) of order at least three, the monophonic distance dm(u, v) is the length of a longest u − v monophonic path in G. A u − v path of length dm(u, v) is called a u − v detour monophonic. For subsets A and B of V, the m-monophonic distance Dm(A, B) is defined as Dm(A, B) = max{dm(x, y) : x ∈ A, y ∈ B}. A u − v path of length Dm(A, B) is called a A − B m-detour monophonic path joining the sets A, B ⊆ V, where u ∈ A and v ∈ B. A set S ⊆ E is called an edge-to-vertex m-detour monophonic set of G if every vertex of G is incident with an edge of S or lies on a m-detour monophonic path joining a pair of edges of S. The edge-to-vertex mdetour monophonic number Dmev(G) of G is the minimum order of its edge-to-vertex m-detour monophonic sets and any edge-to-vertex m-detour monophonic set of order Dmev(G) is an edge-to-vertex mdetour monophonic basis of G. Some general properties satisfied by this parameter are studied. The edge-to-vertex m-detour monophonic number of certain classes of graphs are determined. It is shown that for positive integers r, d and k ≥ 4 with r < d, there exists a connected graph G such that radm(G) = r, diamm(G) = d and Dmev(G) = k | en-US |
| dc.format | application/pdf | |
| dc.language | eng | |
| dc.publisher | Universidad Católica del Norte. | es-ES |
| dc.relation | https://www.revistaproyecciones.cl/article/view/3161/2928 | |
| 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 3 (2018); 415-428 | en-US |
| dc.source | Proyecciones. Revista de Matemática; Vol. 37 Núm. 3 (2018); 415-428 | es-ES |
| dc.source | 0717-6279 | |
| dc.source | 0716-0917 | |
| dc.subject | Monophonic distance | en-US |
| dc.subject | m-detour monophonic path | en-US |
| dc.subject | Edge-to-vertex m-detour monophonic set | en-US |
| dc.subject | Edge-to-vertex m-detour monophonic basis | en-US |
| dc.subject | Edge-to-vertex m-detour monophonic number | en-US |
| dc.title | Edge-to-vertex m-detour 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 |
