Rainbow degree-jump coloring of graphs
| Autor: | E.G. Mphako-Banda, J. Kok, S. Naduvath |
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| Jazyk: | English<br />Ukrainian |
| Rok vydání: | 2021 |
| Předmět: | |
| Zdroj: | Karpatsʹkì Matematičnì Publìkacìï, Vol 13, Iss 1, Pp 229-239 (2021) |
| Druh dokumentu: | article |
| ISSN: | 2075-9827 2313-0210 |
| DOI: | 10.15330/cmp.13.1.229-239 |
| Popis: | 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. |
| Databáze: | Directory of Open Access Journals |
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