A perfect matching is a matching that matches all vertices of the graph.
find the number of perfect matching of following graph :
i think we have two general case:
case 1 perfect matchings in yellow graph as below :
in this case we have only two perfect matchings in any yellow graph so we have $2^4$ perfect matchings
case 2 perfect matchings in white graphs as above. with similar way we have $2^4$ perfect matchings. so we have $2^4+2^4=32$ perfect matchings. is my answer true ?