Siegel, D.; Chen, Y. F. The S-C-L graph in chemical kinetics. (English) Zbl 0827.92027 Rocky Mt. J. Math. 25, No. 1, 479-489 (1995). 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 P. M. Schlosser and 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 F. Horn and R. Jackson [Arch. Rat. Mech. Anal. 47, 81-116 (1972)] and by 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 A. I. Vol’pert and 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. MSC: 92E20 Classical flows, reactions, etc. in chemistry 05C90 Applications of graph theory Keywords:species-complex-linkage graph; standard reaction diagram; deficiency zero theorem; chemical reaction networks Citations:Zbl 0564.46025 PDFBibTeX XMLCite \textit{D. Siegel} and \textit{Y. F. Chen}, Rocky Mt. J. Math. 25, No. 1, 479--489 (1995; Zbl 0827.92027) Full Text: DOI References: [1] J.A. Bondy and U.S.R. Murty, Graph theory with applications , The Macmillan Press, London, 1976. · Zbl 1226.05083 [2] P. Erdi and J. Toth, Mathematical models of chemical reactions , Princeton University Press, New Jersey, 1989. [3] M. Feinberg, Complex balancing in general kinetic systems , Arch. Rational Mech. Anal. 49 (1972), 187-194. [4] ——–, Lectures on chemical reaction networks , Unpublished lectures given at the Mathematics Research Center, University of Wisconsin, 1979. [5] F. Harary, Graph theory , Addison-Wesley Publishing, Massachusetts, 1969. · Zbl 0182.57702 [6] F. Horn and R. Jackson, General mass action kinetics , Arch. Rational Mech. Anal. 47 (1972), 81-116. [7] P.M. Schlosser and M. Feinberg, A graphical determination of the possibility of multiple steady states in complex isothermal CFSTRs , in Complex chemical reaction systems (J. Warnatz and W. Jager, eds.), Springer-Verlag, Berlin, 1987. [8] A.I. Vol’pert and S.I. Hudjaev, Analysis in classes of discontinuous functions and equations of mathematical physics , Chapter 12, Marinus Nijhoff Publishers, Dordrecht, Netherlands, 1985. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.