Subgrpah matching is a basic operation in graph theory. This paper focuses on a variant, namely subgraph matching with inclusion degree (SMID), which retrieves subgraphs that are structurally isomorphic to the query graph while satisfying the condition that the inclusion degree between matched vertexes is greater than a given value. SMID can be applied to many applications, including paper search, crowdsourcing, and recruitment. To efficiently process SMID, this paper designs a novel signature mechanism for data graph and query graph respectively by holding the information of both vertex elements and graph structure. Based on graph signature, a dynamic signature tree (DS-Tree) is built to speed up the SMID processing. A compression method is proposed to reduce the memory usage of DS-Tree. To achieve a better performance, an efficient dominating-set-based subgraph matching algorithm is also developed. Extensive experiments on both real and synthetic datasets demonstrate that the method introduced in this paper outperforms state-of-the-art methods by an order of magnitude in terms of efficiency and scalability.