Rainbow neighbourhood number of graphs

Title

Rainbow neighbourhood number of graphs

Creator

Kok J.; Naduvath S.; Jamil M.K.

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 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.

Source

Proyecciones, Vol-38, No. 3, pp. 470-483.

Date

2019-01-01

Publisher

Universidad Catolica del Norte

Subject

Colour classes; Colour cluster; Expanded line graph; Rainbow neighbourhood; V-clique

Coverage

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

Rights

All Open Access; Gold Open Access; Green Open Access

Relation

ISSN: 7160917

Format

Online

Language

English

Type

Article

Identifier

https://doi.org/10.22199/issn.0717-6279-2019-03-0030

https://www.scopus.com/inward/record.uri?eid=2-s2.0-85069857355&doi=10.22199%2fissn.0717-6279-2019-03-0030&partnerID=40&md5=bd86c8ed8b124434a225efdeea99577b