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Rainbow degree-jump coloring of graphs

2021; Vasyl Stefanyk Prycarpathian National University; Volume: 13; Issue: 1 Linguagem: Inglês

10.15330/cmp.13.1.229-239

2313-0210

Eunice Mphako-Banda, Johan Kok, Sudev Naduvath,

Nuclear Receptors and Signaling

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.