Frequent subgraph mining is fundamental in graph mining, with wide-ranging applications in domains such as biology, chemistry, and social network analysis. Most existing algorithms are tailored for static graph databases. Real-world databases often exhibit dynamic attributes, such as data that may change over time. Existing methods for mining frequent subgraphs in databases with dynamic attributes primarily cater to dynamic graph databases, in which graphs evolve over time. However, in practice, a category of graph databases allows for adding or removing graphs. We refer to these databases as dynamic ones, which can be incrementally or decrementally updated while the remaining graphs do not change. This paper introduces frequent subgraph mining in this type of database and proposes the corresponding algorithm called DyFSM. We design a set called Fringe, which comprises DMFSand DMIS. DMFSis a novel concise representation based on the DFS code and can efficiently recover all frequent subgraphs. DMISis a set of subgraphs from which all infrequent subgraphs can be extended. Fringefacilitates updating frequent subgraphs in the renewed database. In our experiments, we collect four real-world graph datasets and conduct experiments using DyFSM. The results validate the accuracy and show good performance of our algorithm.