The term chemical graphs is often used for labeled undirected graphs that represent chemical structural formulas. Here, we will use it more specifically to refer to the multigraphs that are equivalent to Lewis formulas describing neutral compounds without unpaired electrons. In this setting, each bonding electron pair is represented as an edge, and each non-bonding electron pair as a loop. The bond order is therefore determined by the number of parallel edges. The electron pair of a bond is considered to be divided up between the two atoms that it connects, while a non-bonding pair is localized at a single atom. The number of electrons in the outer shell is usually preserved (at least for the atoms typically appearing in organic chemistry). The atom type therefore defines the degree of a vertex in the multigraph, which is given as the number of incident edges (counting multiplicities) plus twice the number of loops, see Fig. . This standard notion of degree in multigraphs agrees with Frankland's "atomicity" and conforms to the IUPAC term valency . We note in passing that the formalism can be extended in principle to accommodate unpaired electrons and charges e.g. by considering graphs with semi-edges . Here, we will not make use of such extensions, however. The oxidation state of an atom is implicitly determined by the different number of loops and bonds and thus can be changed by converting loops to bonds or vice versa. For example sulfur may have degree two like oxygen, in which case there are two loops. These may be exchanged for bonding electron pairs, as e.g. in SO 3 . For our purposes we disregard oxidation states and thus assume that the number of loops, i.e., non-bonding electron pairs, is also fixed for a given atom type. This amounts to considering loop-free graphs where the degrees are fixed by the atom types. It is not difficult to accommodate also changes in oxidation states by allowing loops to be removed or two cut-edges to be combined to a loop. For ease of presentation, we will not consider this issue further.