A graph theoretical procedure for solving multistep coupled kinetic rate equations and thereby obtaining the concentrations of the species involved in the reaction has been developed. The method so developed has been illustrated with some well-known reaction schemes.

Graph theoretical solutions for kinetic rate equations of some reaction networks involving linear chains and cycles have been derived; condensation polymerization and long chain of radioactive decay come under the purview of the former whereas the interconversion of the species in cycles under the later. The reactions for the linear chains considered here proceed monotonically to the steady states with time whereas the cycle with all irreversible steps has been found to have either periodic or monotonic time evaluation of concentrations depending on the values of rate constants of the involved paths. In case of a cyclic reaction having all reversible paths, the condition for the microscopic reversibility has been derived on the basis of the assumption that the decay constants obtained for this case are all real.

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First order or pseudo-first order reactions involving reversible linear chain and cyclic reaction networks are considered here for obtaining the respective characteristic polynomials (CPs) in analytical forms as well as the recursion relations among the CP coefficients. The zeros of the CP concerned are the decay constants that are useful in expressing the concentrations of the chemical species involved in the chemical reaction network at any instant of time. Illustrations are given for obtaining the CP coefficients of a few such graphs and some consequences thereof are presented. Facile computer programming can be made with these recursion relations for generating such polynomials.

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