Johan Colouring of Graph Operations

Johan Kok; Sudev Naduvath

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arXiv · 1704.02869

Johan Colouring of Graph Operations

Johan Kok·Sudev Naduvath

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Abstract

A vertex $v$ of a given graph is said to be in a rainbow neighbourhood of $G$ if every colour class of $G$ consists of at least one vertex from the closed neighbourhood $N[v]$. A maximal proper colouring of a graph $G$ is a Johan colouring if and only if every vertex of $G$ belongs to a rainbow neighbourhood of $G$. In general all graphs need not have a Johan colouring, even though they admit a chromatic colouring. In this paper, we characterise graphs which admit a Johan colouring. We also discuss some preliminary results in respect of certain graph operations which admit a Johan colouring under certain conditions.

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Johan Kok, Sudev Naduvath. 2017-04-03. Johan Colouring of Graph Operations. https://arxiv.org/abs/1704.02869

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