| dc.creator | Santhakumaran, A. P. | |
| dc.creator | Jebaraj, T. | |
| dc.date | 2020-02-04 | |
| dc.date.accessioned | 2020-02-05T12:59:09Z | |
| dc.date.available | 2020-02-05T12:59:09Z | |
| dc.identifier | https://www.revistaproyecciones.cl/article/view/3984 | |
| dc.identifier | 10.22199/issn.0717-6279-2020-01-0011 | |
| dc.identifier.uri | https://revistaschilenas.uchile.cl/handle/2250/123602 | |
| dc.description | For a connected graph G of order n, a set S of vertices is called a double geodetic set of G if for each pair of vertices x, y in G there exist vertices u, v ∈ S such that x, y ∈ I[u, v]. The double geodetic number dg(G) is the minimum cardinality of a double geodetic set. Any double godetic set of cardinality dg(G) is called a dg-set of G. A connected double geodetic set of G is a double geodetic set S such that the subgraph G[S] induced by S is connected. The mínimum cardinality of a connected double geodetic set of G is the connected double geodetic number of G and is denoted by dgc(G). A connected double geodetic set of cardinality dgc(G) is called a dgc-set of G. A total double geodetic set of a graph G is a double geodetic set S such that the subgraph G[S] induced by S has no isolated vertices. The minimum cardinality of a total double geodetic set of G is the total double geodetic number of G and is denoted by dgt(G). For positive integers r, d and k ≥ 4 with r ≤ d ≤ 2r, there exists a connected graph G with rad G = r, diam G = d and dgt(G) = k. It is shown that if n, a, b are positive integers such that 4 ≤ a ≤ b ≤ n, then there exists a connected graph G of order n with dgt(G) = a and dgc(G) = b. Also, for integers a, b with 4 ≤ a ≤ b and b ≤ 2a, there exists a connected graph G such that dg(G) = a and dgt(G) = b. | en-US |
| dc.format | application/pdf | |
| dc.language | eng | |
| dc.publisher | Universidad Católica del Norte. | en-US |
| dc.relation | https://www.revistaproyecciones.cl/article/view/3984/3337 | |
| dc.rights | Copyright (c) 2020 A. P. Santhakumaran, T. Jebaraj | en-US |
| dc.rights | http://creativecommons.org/licenses/by/4.0 | en-US |
| dc.source | Proyecciones (Antofagasta, On line); Vol 39 No 1 (2020); 167-178 | en-US |
| dc.source | Proyecciones. Revista de Matemática; Vol. 39 Núm. 1 (2020); 167-178 | es-ES |
| dc.source | 0717-6279 | |
| dc.source | 0716-0917 | |
| dc.subject | Geodetic number | en-US |
| dc.subject | Double geodetic number | en-US |
| dc.subject | Connected double geodetic number | en-US |
| dc.subject | Total double geodetic number | en-US |
| dc.subject | 05C12 | en-US |
| dc.subject | Distance in graphs | en-US |
| dc.title | The total double geodetic number of a graph | en-US |
| dc.type | info:eu-repo/semantics/article | |
| dc.type | info:eu-repo/semantics/publishedVersion | |
| dc.type | Peer-reviewed Article | en-US |
| dc.type | text | en-US |
