The graph coloring problem is a well-known combinatorial problem that seeks a coloring pattern such that no two adjacent vertices share the same color. In this paper, we propose an efficient method not only for finding one solution but also for efficiently enumerating all solutions that satisfy the graph coloring constraints. Our method uses ZDDs (Zero-suppressed Binary Decision Diagrams) for efficiently indexing sets of graph coloring patterns. In addition, we propose an algorithm to generate all coloring patterns that do not split any cell of a given set partition. Our experimental results demonstrate that the proposed method significantly outperforms existing solvers. Compared to the leading ASP (Answer Set Programming) solver, our approach generates all coloring patterns more than 1,000 times faster. Our method is applicable to many practical graph instances with up to around 25 vertices, in a feasible computation time.