Existence of a not necessarily symmetric matrix with given distinct eigenvalues and graph

For given distinct numbers λ1±μ1i,λ2±μ2i,…,λk±μki∈C∖R and γ1,γ2,…,γl∈R, and a given graph G with a matching of size at least k, we will show that there is a real matrix whose eigenvalues are the given numbers and its graph is G. In particular, this implies that any real matrix with distinct eigenvalues is similar to a real, irreducible, tridiagonal matrix.