Algebraic operations on graphs preserving the degree sequence

A finite state automaton implementation of the algorithm of a transformation from a given graph to another one with keeping a degree sequence is considered. The algorithm studied here may be used for optimization of computer networks with a given set of providers and restrictions posed on their communication capability. In this case it is sufficient to know only local characteristics of a netwok, but not global ones as it is required in the algorithm of V. Gavel and S. Hakimi.