(untitled) (Journal of Informatics and Mathematical Sciences, 2017)
An acyclic coloring of a graph \(G\) is a proper vertex coloring such that the induced subgraph of any two color classes is acyclic. The minimum number of colors needed to acyclically color the vertices of a graph \(G\) is called as acyclic chromatic number and is denoted by \(χ_a(G)\). In this paper, we give the exact value of the acyclic chromatic number of Mycielskian graph of cycles, paths, complete graphs and complete bipartite graphs.