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

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 closed -contains at least one of each colour of the chromatic colour set, we say that yields a -rainbow neighbourhood.