Rainbow neighbourhood number of graphs
Abstract 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.
| Main Authors: | , , |
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| Format: | Digital revista |
| Language: | English |
| Published: |
Universidad Católica del Norte, Departamento de Matemáticas
2019
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| Online Access: | http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172019000300469 |
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