A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf
.
Generalisation of the rainbow neighbourhood number and 𝑘-jump colouring of a graph
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