A Frobenius Lie algebra g is one on which there exists a linear functional F such that the skew bilinear form B_F defined by B_F(x, y) = F([x, y]) is non-degenerate. Here B_F is a 2-coboundary in the Chevalley-Eilenberg complex for the cohomology of g. More generally, g is quasi-Frobenius if it admits a non-degenerate 2-cocycle B. When that is the case, inverting the matrix of B_F yields a skew solution to the classical Yang-Baxter equation. Let P(n,m) denote the mth maximal parabolic subalgebra of sl(n), i.e., the subalgebra generated by all positive roots and all negative roots except the mth. Elashvili (whose results have been extended by Dergachev and Kirillov) has shown that P(n,m) is Frobenius if and only if (m, n) = 1. In this case we exhibit some explicit forms F for which the induced skew bilinear form B_F on P(n,m) is non-singular and for which (B_F)^−1 can be calculated recursively. In the process we must examine certain graphs determined by F and commutative nilpotent algebras associated with them.