Acyclic graph coloring problems have applications in network design, graph algorithms, and combinatorial optimization. Given two simple, connected, and undirected graphs, G and H, their corona product \(G {\circ } H\) provides a way to combine the structures of G and H while introducing additional interconnections between their vertex sets V(G) and V(H). In this research, the acyclic coloring parameters of G and H, \(\chi _{a}(G)\) and \(\chi _{a}(H)\) , respectively, are analyzed by considering the color classes of V(G) and V(H) in three different cases to find \( \chi _{a}(G {\circ } H)\) , the acyclic coloring of \(G {\circ } H\) . This research also analyzes \( \chi _{a}(G {\circ } H)\) and \( \chi _{a}(H {\circ } G)\) based on \(\chi _{a}(G)\) and \(\chi _{a}(H)\) . This research proves the important result that the maximum degree of \(G {\circ } H\) , \(\Delta (G {\circ } H) = \chi '_{a}(G {\circ } H)\) , the acyclic chromatic index of \(G {\circ } H\) , when G and H satisfy the acyclic edge coloring conjecture.
