@article{Mphako-Banda_Kok_Naduvath_2021, title={Rainbow degree-jump coloring of graphs}, volume={13}, url={https://scijournals.pnu.edu.ua/index.php/cmp/article/view/3918}, DOI={10.15330/cmp.13.1.229-239}, abstractNote={<p>In this paper, we introduce a new notion called the rainbow degree-jump coloring of a graph. For a vertex $v\in V(G)$, let the degree-jump closed neighbourhood of a vertex $v$ be defined as $N_{deg}[v] = \{u:d(v,u)\leq d(v)\}.$ A proper coloring of a graph $G$ is said to be a rainbow degree-jump coloring of $G$ if for all $v$ in $V(G)$, $c(N_{deg}[v])$ contains at least one of each color class. We determine a necessary and sufficient condition for a graph $G$ to permit a rainbow degree-jump coloring. We also determine the rainbow degree-jump chromatic number, denoted by $\chi_{rdj}(G)$, for certain classes of cycle related graphs.</p>}, number={1}, journal={Carpathian Mathematical Publications}, author={Mphako-Banda, E.G. and Kok, J. and Naduvath, S.}, year={2021}, month={Jun.}, pages={229–239} }