Generalisation of the rainbow neighbourhood number and 𝑘-jump colouring of a graph

Johan Kok, Sudev Naduvath, Eunice Gogo Mphako-Banda
2020 Annales Mathematicae et Informaticae  
In this paper, the notions of rainbow neighbourhood and rainbow neighbourhood number of a graph are generalised and further to these generalisations, the notion of a proper -jump colouring of a graph is also introduced. The generalisations follow from the understanding that a closedneighbourhood of a vertex ∈ ( ) denoted, [ ] is the set, [ ] = { : ( , ) ≤ , ∈ N and ≤ ( )}. If the closed -neighbourhood [ ] contains at least one of each colour of the chromatic colour set, we say that yields a -rainbow neighbourhood.
doi:10.33039/ami.2020.02.003 fatcat:4wues4wa7vgurckkk5v3luauqi