Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Title A name given to the resource Articles Article Faculty Publications -Articles Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Title A name given to the resource Rainbow neighbourhood number of graphs Subject The topic of the resource Colour classes; Colour cluster; Expanded line graph; Rainbow neighbourhood; V-clique Description An account of the resource 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 r?(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. 2019 Johan Kokand Sudev Naduvath and Muhammad Kamran Jamil. Creator An entity primarily responsible for making the resource Kok J.; Naduvath S.; Jamil M.K. Source A related resource from which the described resource is derived Proyecciones, Vol-38, No. 3, pp. 470-483. Publisher An entity responsible for making the resource available Universidad Catolica del Norte Date A point or period of time associated with an event in the lifecycle of the resource 2019-01-01 Identifier An unambiguous reference to the resource within a given context <a href="https://doi.org/10.22199/issn.0717-6279-2019-03-0030" target="_blank" rel="noreferrer noopener">https://doi.org/10.22199/issn.0717-6279-2019-03-0030</a> <br /><br /><a href="https://www.scopus.com/inward/record.uri?eid=2-s2.0-85069857355&amp;doi=10.22199%2Fissn.0717-6279-2019-03-0030&amp;partnerID=40&amp;md5=bd86c8ed8b124434a225efdeea99577b" target="_blank" rel="noreferrer noopener">https://www.scopus.com/inward/record.uri?eid=2-s2.0-85069857355&amp;doi=10.22199%2fissn.0717-6279-2019-03-0030&amp;partnerID=40&amp;md5=bd86c8ed8b124434a225efdeea99577b</a> Rights Information about rights held in and over the resource All Open Access; Gold Open Access; Green Open Access Relation A related resource ISSN: 7160917 Format The file format, physical medium, or dimensions of the resource Online Language A language of the resource English Type The nature or genre of the resource Article Coverage The spatial or temporal topic of the resource, the spatial applicability of the resource, or the jurisdiction under which the resource is relevant Kok J., CHRIST (Deemed to be University), Department of Mathematics, Bangalore, Karnataka, 560029, India; Naduvath S., CHRIST (Deemed to be University), Department of Mathematics, Bangalore, Karnataka, 560029, India; Jamil M.K., Riphah International University, Department of Mathematics, Riphah Institute of Computing and Applied Sciences, Lahore, Pakistan