@article{Kok_Naduvath_Jamil_2019, title={Rainbow neighbourhood number of graphs}, volume={38}, url={https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/2833}, DOI={10.22199/issn.0717-6279-2019-03-0030}, abstractNote={<p><em>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 </em><em>?</em><em> 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 r<sub>?</sub>(G). We also introduce the concepts of an expanded line graph of a graph G and a v-clique of v </em><em>?</em><em> 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.</em></p>}, number={3}, journal={Proyecciones (Antofagasta, On line)}, author={Kok, Johan and Naduvath, Sudev and Jamil, Muhammad Kamran}, year={2019}, month={Aug.}, pages={469-484} }