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A rainbow neighbourhood of a graph $G$ with respect to a proper colouring$\C$ of $G$ is the closed neighbourhood $N[v]$ of a vertex $v$ in $G$ such that$N[v]$ consists of vertices from all colour classes in $G$ with respect to$\C$. The number of vertices in $G$ which yield a rainbow neighbourhood of $G$is called its rainbow neighbourhood number. In this paper, we show that allresults known so far about the rainbow neighbourhood number of a graph $G$implicitly refer to a minimum number of vertices which yield rainbowneighbourhoods in respect of the minimum proper colouring where the colours areallocated in accordance with the rainbow neighbourhood convention. Relaxing theaforesaid convention allows for determining a maximum rainbow neighbourhoodnumber of a graph $G$. We also establish the fact that the minimum and maximumrainbow neighbourhood numbers are respectively, unique and therefore a constantfor a given graph.

Reflection on rainbow neighbourhood numbers of graphs