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".