Matching counting theory is an important part of graph theory and also a active research field. It has not only many applications background

and also the source of many important ideas developed during the rapid growth of combinatorics during the last several decades. But the problem of counting the number of perfect matchings for general graphs is NP-hard. By applying differentiation

summation and re-recursion calculation

several counting formulas of the perfect matchings for two specific types of graphs are given. By the method presented in this paper

the number of all perfect matchings of many graphs can be calculated.