| dc.creator | Kok, Johan | |
| dc.creator | Naduvath, Sudev | |
| dc.creator | Jamil, Muhammad Kamran | |
| dc.date | 2019-08-14 | |
| dc.date.accessioned | 2019-11-14T12:01:13Z | |
| dc.date.available | 2019-11-14T12:01:13Z | |
| dc.identifier | https://www.revistaproyecciones.cl/article/view/2833 | |
| dc.identifier | 10.22199/issn.0717-6279-2019-03-0030 | |
| dc.identifier.uri | https://revistaschilenas.uchile.cl/handle/2250/113629 | |
| dc.description | In this paper, we introduce the notion of the rainbow neighbourhood and a related graph parameter namely the rainbow neighbourhood number and report on preliminary results thereof. The closed neighbourhood N [v] of a vertex v ∈ V (G) which contains at least one coloured vertex of each colour in the chromatic colouring of a graph is called a rainbow neighbourhood. The number of rainbow neighbourhoods in a graph G is called the rainbow neighbourhood number of G, denoted by rχ(G). We also introduce the concepts of an expanded line graph of a graph G and a v-clique of v ∈ V (G). With the help of these new concepts, we also establish a necessary and sufficient condition for the existence of a rainbow neighbourhood in the line graph of a graph G. | 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/2833/3216 | |
| dc.rights | Derechos de autor 2019 Johan Kok, Sudev Naduvath and Muhammad Kamran Jamil | es-ES |
| dc.rights | https://creativecommons.org/licenses/by/4.0 | es-ES |
| dc.source | Proyecciones. Journal of Mathematics; Vol 38 No 3 (2019); 469-484 | en-US |
| dc.source | Proyecciones. Revista de Matemática; Vol. 38 Núm. 3 (2019); 469-484 | es-ES |
| dc.source | 0717-6279 | |
| dc.source | 0716-0917 | |
| dc.subject | Colour cluster | en-US |
| dc.subject | Colour classes | en-US |
| dc.subject | Rainbow neighbourhood | en-US |
| dc.subject | Expanded line graph | en-US |
| dc.subject | v-clique | en-US |
| dc.subject | Degree sequences | en-US |
| dc.subject | 05C07 | en-US |
| dc.subject | Paths and cycles | en-US |
| dc.subject | 05C38 | en-US |
| dc.subject | Structural characterization of types of graphs | en-US |
| dc.subject | 05C75 | en-US |
| dc.subject | Graph algorithms | en-US |
| dc.subject | 05C85 | en-US |
| dc.title | Rainbow neighbourhood number of graphs | en-US |
| dc.type | info:eu-repo/semantics/article | |
| dc.type | info:eu-repo/semantics/publishedVersion | |
| dc.type | Artículo revisado por pares | es-ES |
