Graphs have become popular for modeling structured data. As a result, graph indexing technique has come to play an essential role in query processing. This paper investigates the issues of indexing graphs and propose an approximation solution. The proposed approach, called MSTA, makes use of minimal spanning tree as basic indexing feature. By containment relation of edge lists and maximal common subgraph based graph distance, those minimal spanning trees are organized into an indexing structure named MST tree. MST tree can support many kinds of queries efficiently, such as subgraph queries. The performance study shows that index size and constructing time of traditional methods are tens or even a hundred times larger than MSTA.