TY - JOUR
AU - Mphako-Banda, E.G.
AU - Kok, J.
AU - Naduvath, S.
PY - 2021/06/30
Y2 - 2024/04/19
TI - Rainbow degree-jump coloring of graphs
JF - Carpathian Mathematical Publications
JA - Carpathian Math. Publ.
VL - 13
IS - 1
SE - Scientific articles
DO - 10.15330/cmp.13.1.229-239
UR - https://scijournals.pnu.edu.ua/index.php/cmp/article/view/3918
SP - 229-239
AB - <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>
ER -