### On the number of dissimilar pfaffian orientations of graphs

A subgraph of a graph is if has a perfect matching. An orientation of is if, for every conformal even circuit , the number of edges of whose directions in agree with any prescribed sense of orientation of is odd. A graph is if it has a Pfaffian orientation. Not every graph is Pfaffian. However, if has a Pfaffian orientation , then the determinant of the adjacency matrix of is the square of the number of perfect matchings of . (See the book by Lovász and Plummer [. Annals of Discrete...