Making a good matching between two-layer vertices is one of the most important problems not only in mathematics but also in practical situations. There are a huge number of candidates for matching solutions in a graph. Each vertex has its own preference list of vertices in the other side. If vertices are matched to dislikes or they feel that they could get more appropriate partner, they may complain of an obtained matching result. Furthermore, the matching result should not have unfairness between vertices.
In this research, we consider to enumerate all possible matchings by using ZDD, which is a data structure for representing a set family, in order to offer good choices in large scale matching problems. We observe that the method based on an ALLSAT solver is faster than the ZDD method in terms of enumeration of complete and stable matchings. We further reveal the relation between the number of matching solutions and the blocking pair capacity, and we confirm that instances with at most 40 vertices are able to solve by our proposal algorithm and enumeration of equitable matchings is relatively faster than that of $k$-blocked matchings.