Abstract
Extending the basic formalism described in a closely related article, this paper defines the reduced equations of a graph model and presents various theoretical results involving those equations, both diophantine and modular. The reduced equations contribute to clarify the existence (or non-existence) of certain types of identities, for some classes of models (a number of which is analysed in the second part of this paper).It is also pointed out that there exist systems of equations (related to the reduced equations) that can replace the system of constituent equations for the purpose of deriving the identities of a given model. A definite diophantine system is proposed, one for which the coefficient matrix is typically smaller than that of the system of constituent equations.
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