[Recurrent relationship for the characteristic polynom of a system of enzymatic catalysis of nonbranched monomolecular reactions].

A new mode is proposed to represent the characteristics equation for the system of monomolecular reaction on the basis of directed graphs method. A characteristic equation can be represented as a sum of weights of spanning trees derived from some graph which is connected with the initial graph of reaction. The recurrent relationship for the characteristic polynom of the system of nonbranched monomolecular reaction was obtained on the basis of this representation. A new proof on the matrix theorem about trees formulated by Volkenstein and Goldstein was established.