The increasing computational demand promotes the application of parallel tasks with complex execution dependencies in industrial applications. The Directed Acyclic Graph (DAG) task model is widely applied with dedicated scheduling algorithms to understand and manage the execution of such systems. In order to validate the effectiveness of different DAG scheduling algorithms, DAG generators are often applied to produce synthesized DAGs for performance evaluation. However, existing DAG generators either fail to provide sufficient topology coverage or suffer from severe scalability issues, leading to biased and incomplete evaluation results. This paper proposes a novel DAG generator that provides full topology coverage under the given DAG structural parameters while eliminating isomorphic DAGs as well as redundant edges in each DAG. In addition, a verification method is constructed that enables topology coverage, isomorphic DAG identification, and constraint satisfaction of the generated DAGs. The experimental results show that compared to existing generators, the proposed DAG generator achieves full topology coverage and significantly reduces the number of DAGs being produced. The DAG generator proposed in this work provides a complete solution for synthesised DAG generation, enabling fair and comprehensive evaluation of DAG systems.