An algorithm for the construction of the graphs of organic molecules.

A description and a formal proof of an efficient computer implemented algorithm for the construction of graphs is presented. This algorithm, which is part of a program for the automated analysis of organic compounds, constructs all of the non-isomorphic, connected multi- graphs based on a given degree sequence of nodes and which arise from a relatively small ''catalog'' of certain canonical graphs. For the graphs of the more common organic molecules, a catalog of most of the canonical graphs is known, and the algorithm can produce all of the distinct valence isomers of these organic molecules.