  The curling number of a graph G is defined as the number of times an element
in the degree sequence of G appears the maximum. Graph colouring is an
assignment of colours, labels or weights to the vertices or edges of a graph. A
colouring $\mathcal{C}$ of colours $c_1,c_2,\ldots,c_l$ is said to be a minimum
parameter colouring if C consists of a minimum number of colours with smallest
subscripts. In this paper, we study colouring version of curling number of
certain graphs, with respect to their minimum parameter colourings.
