Rainbow degree-jump coloring of graphs

  • E.G. Mphako-Banda University of Witswatersrand, Johannesburg, South Africa
  • J. Kok CHRIST (Deemed to be University), Bangalore, Karnataka, India
  • S. Naduvath CHRIST (Deemed to be University), Bangalore, Karnataka, India
Keywords: rainbow degree-jump coloring, rainbow degree-jump chromatic number, blind vertex, Mphako graph, Moore bound
Published online: 2021-06-30

Abstract


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.

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How to Cite
(1)
Mphako-BandaE., Kok J., Naduvath S. Rainbow Degree-Jump Coloring of Graphs. Carpathian Math. Publ. 2021, 13 (1), 229-239.