Abstract.
This work connects the Graph Theory with the Matrix Theory. We
demonstrate that every $^{(h,j)}G$ digraph of one multidigraph
$k$-regular of $n$ vertexs has exactly $[k^{(h-j)}!]^{n \cdot
k^j}$ different covering subdigraphs $(k^{(h-j)}-1)$-regulars. The
demonstration is via a suitable matrix representation, using the
permanent of the precedence matrix of the $(h,j)$ adjoint
digraphs".
