The S-C-L graph in chemical kinetics (Q1898328)

The structure of certain graphs induced by chemical reaction networks plays a vital role in the study of chemical kinetics. In this paper the Species-Complex-Linkage (S-C-L) graph which was first introduced by \textit{P. M. Schlosser} and \textit{M. Feinberg} [in J. Warnatz and W. Jager (eds.), Complex chemical reaction systems (1987)] will be related to two other graphs, namely, the HJF-graph (standard reaction diagram) studied by \textit{F. Horn} and \textit{R. Jackson} [Arch. Rat. Mech. Anal. 47, 81-116 (1972)] and by \textit{M. Feinberg} [ibid. 49, 187-194 (1972)], and the \(V\)- graph introduced by Vol'pert. The Deficiency Zero Theorem by Horn, Jackson, and Feinberg and a theorem due to Vol'pert [see \textit{A. I. Vol'pert} and \textit{S. I. Khudyaev}, Analysis in classes of discontinuous functions and equations of mathematical physics. (1985; Zbl 0564.46025)] give significant information about the qualitative behavior of certain chemical kinetics systems of mass action type based upon their graphical strucure. Our results here provide sufficient conditions for the applicability of the two theorems.