  Consider a network $D$ of pipes which have to be cleaned using some cleaning
agents, called brushes, assigned to some vertices. The tattooing of a simple
connected directed graph $D$ is a particular type of the cleaning in which an
arc are coloured by the colour of the colour-brush transiting it and the tattoo
number of $D$ is a corresponding derivative of brush numbers in it. In this
paper, we introduce a new concept, called the tattoo index of a given graph
$G$, which is an efficiency index related to the tattooing sequence and we
establish some introductory results on this parameter.
