An acyclic coloring of a graph is a proper coloring without bichromatic cycles such that the union of any two color classes results in a forest. The concept of acyclic coloring is crucial in the computation of Hessians, classification of kekule structures, statistical mechanics and coding theory. In this paper, the acyclic coloring parameters for the Mycielskian of graphs have been computed. Moreover, the relation between the acyclic coloring parameters have been determined for the graphs under consideration. Also, algorithms have been developed for the acyclic coloring of the above-mentioned graphs