Complexity index for the linear mechanisms of chemical reactions

A complexity measure is proposed for the kinetic models of chemical reactions with linear mechanisms. The index is related to the structure of fractional-rational kinetic laws for chemical reactions, as well as to the structure of cyclic graphs used to describe them. The complexity index is shown to be closely related to the detailed hierarchical classification and to the code of linear reaction mechanisms, recently introduced. A number of index properties are proved for two- and three-reaction routes. They reflect the influence of the various classification criteria, such as the number of reaction routes and intermediates, the type, class and subclasses of the mechanism, and the number of intermediates in each reaction route. Hierarchical levels of mechanisms with the same complexity (isocomplex mechanisms) are specified. Standard tables are presented with complexity indices for all topologically distinct linear reaction mechanisms having one to three reaction routes, two to six intermediates, and reversible elementary steps.[/p]