Studing the Hamiltonian circuits of digraph using adjacency matrix

the sufficient and necessary condition of strict digraph to be directedly Hamilton is discussed. Let \%A\% be adjacency matrix of strict digraph

then a sufficient and essential condition of \%D\% to be directedly Hamiltonian graph is that there at least exists a nonitem (-1)\+\{\%τ(j\-1j\-2\:j\-n)+τ(j\-2j\-3\:j\-nj\-1)\}a\-\{j\-1j\-2\}a\-\{j\-2j\-3\}\:a\-\{j\-nj\-1\}\% in expansion of the determinant of \%A\%.