| dc.creator | Santhakumaran, A. P. | |
| dc.creator | Titus, P. | |
| dc.creator | Ganesamoorthy, K. | |
| dc.date | 2017-06-02 | |
| dc.identifier | http://www.revistaproyecciones.cl/article/view/1642 | |
| dc.identifier | 10.4067/S0716-09172017000200209 | |
| dc.description | For a connected graph G = (V, E) of order at least two, a chord of a path P is an edge joining two non-adjacent vertices of P. A path P is called a monophonic path if it is a chordless path. A longest x – y monophonic path is called an x – y detour monophonic path. A set S of vertices of G is a detour monophonic set of G if each vertex v of G lies on an x - y detour monophonic path for some x and y in S. The minimum cardinality of a detour monophonic set of G is the detour monophonic number of G and is denoted by dm(G). A total detour monophonic set of a graph G is a detour monophonic set S such that the subgraph induced by S has no isolated vertices. The minimum cardinality of a total detour monophonic set of G is the total detour monophonic number of G and is denoted by dmt(G). A total detour monophonic set of cardinality dmt(G) is called a dmt-set of G. We determine bounds for it and characterize graphs which realize the lower bound. It is shown that for positive integers r, d and k ≥ 6 with r < d there exists a connected graph G with monophonic radius r, monophonic diameter d and dmt(G) = k. For positive integers a, b such that 4 ≤ a ≤ b with b ≤ 2a, there exists a connected graph G such that dm(G) = a and dmt(G) = b. Also, if p, d and k are positive integers such that 2 ≤ d ≤ p - 2, 3 ≤ k ≤ p and p – d – k + 3 ≥ 0, there exists a connected graph G of order p, monophonic diameter d and dmt(G) = k. | en-US |
| dc.format | application/pdf | |
| dc.language | spa | |
| dc.publisher | Universidad Católica del Norte. | es-ES |
| dc.relation | http://www.revistaproyecciones.cl/article/view/1642/2046 | |
| dc.rights | Derechos de autor 2017 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 36 No 2 (2017); 209-224 | en-US |
| dc.source | Proyecciones. Revista de Matemática; Vol. 36 Núm. 2 (2017); 209-224 | es-ES |
| dc.source | 0717-6279 | |
| dc.source | 0716-0917 | |
| dc.title | The total 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 |
