A diverse collection of edit operations on graphs have been used in the literature, see e.g. . They share the property that they introduce small, local changes into a graph. Thus they can immediately serve as mutation operators in a GA. A non-exhaustive lists can be found in the Appendix. There are, however, several issues with these standard operations when applied to molecular graphs: Some of these operators (including vertex addition, node splitting, or edge deletion) do not preserve connectedness. It is of course possible to restrict these operations such that only connected graphs are produced. For example, node-splitting could be restricted to vertices that are not cut-vertices. Nevertheless, these operations are not readily applicable to chemical graphs, because in general they are not degree preserving. The only exception is node splitting of a vertex with even degree, where one could use operations of the form R O R to R O O R and C to C C such that each of the two carbons inherits two of the original carbons' substituents.