  In this paper we discuss the question of how to decide when a general
chemical reaction system is incapable of admitting multiple equilibria,
regardless of parameter values such as reaction rate constants, and regardless
of the type of chemical kinetics, such as mass-action kinetics,
Michaelis-Menten kinetics, etc. Our results relate previously described linear
algebraic and graph-theoretic conditions for injectivity of chemical reaction
systems. After developing a translation between the two formalisms, we show
that a graph-theoretic test developed earlier in the context of systems with
mass action kinetics, can be applied to reaction systems with arbitrary
kinetics. The test, which is easy to implement algorithmically, and can often
be decided without the need for any computation, rules out the possibility of
multiple equilibria for the systems in question.
