Characteristic polynomials of Straffin digraphs Original Research Article

Let f be a continuous scalar function that permutes a finite subset of the real line. Straffin introduced an associated digraph to study these functions. For a cyclic permutation [so the finite subset is a periodic solution to the xi+1 = f(xi)], we show that the coefficients of the characteristic polynomial of this digraph are odd. This is generalized to give the parity of the coefficients of the characteristic polynomial of the associated digraph of any permutation.