On the number of Euler trails in directed graphs - Jonsson, Jakob (Mathematica Scandinavica, 2002)
Let G be an Eulerian digraph with all in- and out-degrees equal to 2, and let π be an Euler trail in G. We consider an intersection matrix L(π) with the property that the determinant of L(π) + I is equal to the number of Euler trails in G; I denotes the identity matrix. We show that if the inverse of L(π) exists, then L^-1(π) = L(σ) for a certain Euler trail σ in G. Furthermore, we use properties of the intersection matrix to prove some results about how to divide the set of Euler trails in a digraph into smaller sets of the same size.